To see the other types of publications on this topic, follow the link: Group theory and generalizations.
Dissertations / Theses on the topic 'Group theory and generalizations'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Group theory and generalizations.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Byler, Katherine S. "Generalizations of the bias invariant /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3102156.
Full textAbstract:
Thesis (Ph. D.)--University of Oregon, 2003.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 139-141). Also available for download via the World Wide Web; free to University of Oregon users.
2
Zhang, Xiankun. "Generalizations of colorability and connectivity of graphs." Morgantown, W. Va. : [West Virginia University Libraries], 1998. http://etd.wvu.edu/templates/showETD.cfm?recnum=333.
Full textAbstract:
Thesis (Ph. D.)--West Virginia University, 1998.Title from document title page. Document formatted into pages; contains vii, 97 p. : ill. Includes abstract. Includes bibliographical references (p. 93-96).
3
Semeraro, Jason P. G. "Centralisers and amalgams of saturated fusion systems." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:43d7d6d0-363b-4bc7-b17f-5713cc586737.
Full textAbstract:
In this thesis, we mainly address two contrasting topics in the area of saturated fusion systems. The first concerns the notion of a centraliser of a subsystem E of a fusion system F, and we give new proofs of the existence of such an object in the case where E is normal in F. The second concerns the development of the theory of `trees of fusion systems', an analogue for fusion systems of Bass-Serre theory for finite groups. A major theorem finds conditions on a tree of fusion systems for there to exist a saturated completion, and this is applied to construct and classify certain fusion systems over p-groups with an abelian subgroup of index p. Results which do not fall into either of the above categories include a new proof of Thompson's normal p-complement Theorem for saturated fusion systems and characterisations of certain quotients of fusion systems which possess a normal subgroup.
4
Kuckuck, Benno. "Finiteness properties of fibre products." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:a9624d17-9d11-4bd0-8c46-78cbba73469c.
Full textAbstract:
A group Γ is of type Fn for some n ≥ 1 if it has a classifying complex with finite n-skeleton. These properties generalise the classical notions of finite generation and finite presentability. We investigate the higher finiteness properties for fibre products of groups.
5
Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.
Full textAbstract:
The conjugacy length function of a group Γ determines, for a given a pair of conjugate elements u,v ∈ Γ, an upper bound for the shortest γ in Γ such that uγ = γv, relative to the lengths of u and v. This thesis focuses on estimating the conjugacy length function in certain finitely generated groups. We first look at a collection of solvable groups. We see how the lamplighter groups have a linear conjugacy length function; we find a cubic upper bound for free solvable groups; for solvable Baumslag--Solitar groups it is linear, while for a larger family of abelian-by-cyclic groups we get either a linear or exponential upper bound; also we show that for certain polycyclic metabelian groups it is at most exponential. We also investigate how taking a wreath product effects conjugacy length, as well as other group extensions. The Magnus embedding is an important tool in the study of free solvable groups. It embeds a free solvable group into a wreath product of a free abelian group and a free solvable group of shorter derived length. Within this thesis we show that the Magnus embedding is a quasi-isometric embedding. This result is not only used for obtaining an upper bound on the conjugacy length function of free solvable groups, but also for giving a lower bound for their Lp compression exponents. Conjugacy length is also studied between certain types of elements in lattices of higher-rank semisimple real Lie groups. In particular we obtain linear upper bounds for the length of a conjugator from the ambient Lie group within certain families of real hyperbolic elements and unipotent elements. For the former we use the geometry of the associated symmetric space, while for the latter algebraic techniques are employed.
6
Wellen, George Arthur. "Branch groups and automata." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:b0be5468-cce9-421b-85be-c386d7c3808a.
Full textAbstract:
The focus of this thesis is finitely generated subgroups of the automorphism group of an infinite spherically homogeneous rooted tree (regular or irregular). The first chapter introduces the topic and outlines the main results. The second chapter provides definitions of the terminology used, and also some preliminary results. The third chapter introduces a group that appears to be a promising candidate for a finitely generated group of infinite upper rank with finite upper $p$-rank for all primes $p$. It goes on to demonstrate that in fact this group has infinite upper $p$-rank for all primes $p$. As a by-product of this construction, we obtain a finitely generated branch group with quotients that are virtually-(free abelian of rank $n$) for arbitrarily large $n$. The fourth chapter gives a complete classification of ternary automata with $C_2$-action at the root, and a partial classification of ternary automata with $C_3$-action at the root. The concept of a `windmill automaton' is introduced in this chapter, and a complete classification of binary windmill automata is given. The fifth chapter contains a detailed study of the non-abelian ternary automata with $C_3$-action at the root. It also contains some conjectures about possible isomorphisms between these groups.
7
Kielak, Dawid. "Free and linear representations of outer automorphism groups of free groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:f2045fba-1546-4dd3-af9f-7d02c4fc505e.
Full textAbstract:
For various values of n and m we investigate homomorphisms from Out(F_n) to Out(F_m) and from Out(F_n) to GL_m(K), i.e. the free and linear representations of Out(F_n) respectively. By means of a series of arguments revolving around the representation theory of finite symmetric subgroups of Out(F_n) we prove that each homomorphism from Out(F_n) to GL_m(K) factors through the natural map p_n from Out(F_n) to GL(H_1(F_n,Z)) = GL_n(Z) whenever n=3, m < 7 and char(K) is not an element of {2,3}, and whenever n>5, m< n(n+1)/2 and char(K) is not an element of {2,3,...,n+1}. We also construct a new infinite family of linear representations of Out(F_n) (where n > 2), which do not factor through p_n. When n is odd these have the smallest dimension among all known representations of Out(F_n) with this property. Using the above results we establish that the image of every homomorphism from Out(F_n) to Out(F_m) is finite whenever n=3 and n < m < 6, and of cardinality at most 2 whenever n > 5 and n < m < n(n-1)/2. We further show that the image is finite when n(n-1)/2 -1 < m < n(n+1)/2. We also consider the structure of normal finite index subgroups of Out(F_n). If N is such then we prove that if the derived subgroup of the intersection of N with the Torelli subgroup T_n < Out(F_n) contains some term of the lower central series of T_n then the abelianisation of N is finite.
8
Craven, David Andrew. "Algebraic modules for finite groups." Thesis, University of Oxford, 2007. http://ora.ox.ac.uk/objects/uuid:7f641b33-d301-4445-8269-a5a33f4b7e5e.
Full textAbstract:
The main focus of this thesis is algebraic modules---modules that satisfy a polynomial equation with integer co-efficients in the Green ring---in various finite groups, as well as their general theory. In particular, we ask the question `when are all the simple modules for a finite group G algebraic?' We call this the (p-)SMA property. The first chapter introduces the topic and deals with preliminary results, together with the trivial first results. The second chapter provides the general theory of algebraic modules, with particular attention to the relationship between algebraic modules and the composition factors of a group, and between algebraic modules and the Heller operator and Auslander--Reiten quiver. The third chapter concerns itself with indecomposable modules for dihedral and elementary abelian groups. The study of such groups is both interesting in its own right, and can be applied to studying simple modules for simple groups, such as the sporadic groups in the final chapter. The fourth chapter analyzes the groups PSL(2,q); here we determine, in characteristic 2, which simple modules for PSL(2,q) are algebraic, for any odd q. The fifth chapter generalizes this analysis to many groups of Lie type, although most results here are in defining characteristic only. Notable exceptions include the small Ree groups, which have the 2-SMA property for all q. The sixth and final chapter focuses on the sporadic groups: for most groups we provide results on some simple modules, and some of the groups are completely analyzed in all characteristics. This is normally carried out by restricting to the Sylow p-subgroup. This thesis develops the current state of knowledge concerning algebraic modules for finite groups, and particularly for which simple groups, and for which primes, all simple modules are algebraic.
9
Wharton, Elizabeth. "The model theory of certain infinite soluble groups." Thesis, University of Oxford, 2006. http://ora.ox.ac.uk/objects/uuid:7bd8d05b-4ff6-4326-8463-f896e2862e25.
Full textAbstract:
This thesis is concerned with aspects of the model theory of infinite soluble groups. The results proved lie on the border between group theory and model theory: the questions asked are of a model-theoretic nature but the techniques used are mainly group-theoretic in character. We present a characterization of those groups contained in the universal closure of a restricted wreath product U wr G, where U is an abelian group of zero or finite square-free exponent and G is a torsion-free soluble group with a bound on the class of its nilpotent subgroups. For certain choices of G we are able to use this characterization to prove further results about these groups; in particular, results related to the decidability of their universal theories. The latter part of this work consists of a number of independent but related topics. We show that if G is a finitely generated abelian-by-metanilpotent group and H is elementarily equivalent to G then the subgroups gamma_n(G) and gamma_n(H) are elementarily equivalent, as are the quotient groups G/gamma_n(G) and G/gamma_n(H). We go on to consider those groups universally equivalent to F_2(VN_c), where the free groups of the variety V are residually finite p-groups for infinitely many primes p, distinguishing between the cases when c = 1 and when c > 2. Finally, we address some important questions concerning the theories of free groups in product varieties V_k · · ·V_1, where V_i is a nilpotent variety whose free groups are torsion-free; in particular we address questions about the decidability of the elementary and universal theories of such groups. Results mentioned in both of the previous two paragraphs have applications here.
10
Riley, Timothy Rupert. "Asymptotic invariants of infinite discrete groups." Thesis, University of Oxford, 2002. http://ora.ox.ac.uk/objects/uuid:30f42f4c-e592-44c2-9954-7d9e8c1f3d13.
Full textAbstract:
Asymptotic cones. A finitely generated group has a word metric, which one can scale and thereby view the group from increasingly distant vantage points. The group coalesces to an "asymptotic cone" in the limit (this is made precise using techniques of non-standard analysis). The reward is that in place of the discrete group one has a continuous object "that is amenable to attack by geometric (e.g. topological, infinitesimal) machinery" (to quote Gromov). We give coarse geometric conditions for a metric space X to have N-connected asymptotic cones. These conditions are expressed in terms of certain filling functions concerning filling N-spheres in an appropriately coarse sense. We interpret the criteria in the case where X is a finitely generated group Γ with a word metric. This leads to upper bounds on filling functions for groups with simply connected cones -- in particular they have linearly bounded filling length functions. We prove that if all the asymptotic cones of Γ are N-connected then Γ is of type FN+1 and we provide N-th order isoperimetric and isodiametric functions. Also we show that the asymptotic cones of a virtually polycyclic group Γ are all contractible if and only if Γ is virtually nilpotent. Combable groups and almost-convex groups. A combing of a finitely generated group Γ is a normal form; that is a choice of word (a combing line) for each group element that satisfies a geometric constraint: nearby group elements have combing lines that fellow travel. An almost-convexity condition concerns the geometry of closed balls in the Cayley graph for Γ. We show that even the most mild combability or almost-convexity restrictions on a finitely presented group already force surprisingly strong constraints on the geometry of its word problem. In both cases we obtain an n! isoperimetric function, and upper bounds of ~ n2 on both the minimal isodiametric function and the filling length function.
11
Fink, Elisabeth. "On some non-periodic branch groups." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e8aec0f9-e60f-457c-87d1-0780720e2cae.
Full text
12
Bogdanic, Dusko. "Graded blocks of group algebras." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:faeaaeab-1fe6-46a9-8cbb-f3f633131a73.
Full textAbstract:
In this thesis we study gradings on blocks of group algebras. The motivation to study gradings on blocks of group algebras and their transfer via derived and stable equivalences originates from some of the most important open conjectures in representation theory, such as Broue’s abelian defect group conjecture. This conjecture predicts the existence of derived equivalences between categories of modules. Some attempts to prove Broue’s conjecture by lifting stable equivalences to derived equivalences highlight the importance of understanding the connection between transferring gradings via stable equivalences and transferring gradings via derived equivalences. The main idea that we use is the following. We start with an algebra which can be easily graded, and transfer this grading via derived or stable equivalence to another algebra which is not easily graded. We investigate the properties of the resulting grading. In the first chapter we list the background results that will be used in this thesis. In the second chapter we study gradings on Brauer tree algebras, a class of algebras that contains blocks of group algebras with cyclic defect groups. We show that there is a unique grading up to graded Morita equivalence and rescaling on an arbitrary basic Brauer tree algebra. The third chapter is devoted to the study of gradings on tame blocks of group algebras. We study extensively the class of blocks with dihedral defect groups. We investigate the existence, positivity and tightness of gradings, and we classify all gradings on these blocks up to graded Morita equivalence. The last chapter deals with the problem of transferring gradings via stable equivalences between blocks of group algebras. We demonstrate on three examples how such a transfer via stable equivalences is achieved between Brauer correspondents, where the group in question is a TI group.
13
Childers, Kristen Snyder. "Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type Spaces." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3042.
Full textAbstract:
In [2], Beals, Gaveau and Greiner find the fundamental solution to a 2-Laplace-type equation in a class of sub-Riemannian spaces. This fundamental solution is based on the well-known fundamental solution to the p-Laplace equation in Grushin-type spaces [4] and the Heisenberg group [6]. In this thesis, we look to generalize the work in [2] for a p-Laplace-type equation. After discovering that the "natural" generalization fails, we find two generalizations whose solutions are based on the fundamental solution to the p-Laplace equation.
14
Sisto, Alessandro. "Geometric and probabilistic aspects of groups with hyperbolic features." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:bcf456c4-eef0-4fe8-bb7d-8b15f9cf7b18.
Full textAbstract:
The main objects of interest in this thesis are relatively hyperbolic groups. We will study some of their geometric properties, and we will be especially concerned with geometric properties of their boundaries, like linear connectedness, avoidability of parabolic points, etc. Exploiting such properties will allow us to construct, under suitable hypotheses, quasi-isometric embeddings of hyperbolic planes into relatively hyperbolic groups and quasi-isometric embeddings of relatively hyperbolic groups into products of trees. Both results have applications to fundamental groups of 3-manifolds. We will also study probabilistic properties of relatively hyperbolic groups and of groups containing ``hyperbolic directions'' despite not being relatively hyperbolic, like mapping class groups, Out(Fn), CAT(0) groups and subgroups of the above. In particular, we will show that the elements that generate the ``hyperbolic directions'' (hyperbolic elements in relatively hyperbolic groups, pseudo-Anosovs in mapping class groups, fully irreducible elements in Out(Fn) and rank one elements in CAT(0) groups) are generic in the corresponding groups (provided at least one exists, in the case of CAT(0) groups, or of proper subgroups). We also study how far a random path can stray from a geodesic in the context of relatively hyperbolic groups and mapping class groups, but also of groups acting on a relatively hyperbolic space. We will apply this, for example, to show properties of random triangles.
15
Tarrago, Pierre. "Non-commutative generalization of some probabilistic results from representation theory." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1123/document.
Full textAbstract:
Le sujet de cette thèse est la généralisation non-commutative de résultats probabilistes venant de la théorie des représentations. Les résultats obtenus se divisent en trois parties distinctes. Dans la première partie de la thèse, le concept de groupe quantique easy est étendu au cas unitaire. Tout d'abord, nous donnons une classification de l'ensemble des groupes quantiques easy unitaires dans le cas libre et classique. Nous étendons ensuite les résultats probabilistes de au cas unitaire. La deuxième partie de la thèse est consacrée à une étude du produit en couronne libre. Dans un premier temps, nous décrivons les entrelaceurs des représentations dans le cas particulier d'un produit en couronne libre avec le groupe symétrique libre: cette description permet également d'obtenir plusieurs résultats probabilistes. Dans un deuxième temps, nous établissons un lien entre le produit en couronne libre et les algèbres planaires: ce lien mène à une preuve d'une conjecture de Banica et Bichon. Dans la troisième partie de la thèse, nous étudions un analoque du graphe de Young qui encode la structure multiplicative des fonctions fondamentales quasi-symétriques. La frontière minimale de ce graphe a déjà été décrite par Gnedin et Olshanski. Nous prouvons que la frontière minimale coïncide avec la frontière de Martin. Au cours de cette preuve, nous montrons plusieurs résultats combinatoires asymptotiques concernant les diagrammes de Young en rubanThe subject of this thesis is the non-commutative generalization of some probabilistic results that occur in representation theory. The results of the thesis are divided into three different parts. In the first part of the thesis, we classify all unitary easy quantum groups whose intertwiner spaces are described by non-crossing partitions, and develop the Weingarten calculus on these quantum groups. As an application of the previous work, we recover the results of Diaconis and Shahshahani on the unitary group and extend those results to the free unitary group. In the second part of the thesis, we study the free wreath product. First, we study the free wreath product with the free symmetric group by giving a description of the intertwiner spaces: several probabilistic results are deduced from this description. Then, we relate the intertwiner spaces of a free wreath product with the free product of planar algebras, an object which has been defined by Bisch and Jones. This relation allows us to prove the conjecture of Banica and Bichon. In the last part of the thesis, we prove that the minimal and the Martin boundaries of a graph introduced by Gnedin and Olshanski are the same. In order to prove this, we give some precise estimates on the uniform standard filling of a large ribbon Young diagram. This yields several asymptotic results on the filling of large ribbon Young diagrams
16
Laugwitz, Robert. "Braided Hopf algebras, double constructions, and applications." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:ddcb459f-c3b4-40dd-9936-6bad6993ce8c.
Full textAbstract:
This thesis contains four related papers which study different aspects of double constructions for braided Hopf algebras. The main result is a categorical action of a braided version of the Drinfeld center on a Heisenberg analogue, called the Hopf center. Moreover, an application of this action to the representation theory of rational Cherednik algebras is considered. Chapter 1 : In this chapter, the Drinfeld center of a monoidal category is generalized to a class of mixed Drinfeld centers. This gives a unified picture for the Drinfeld center and a natural Heisenberg analogue. Further, there is an action of the former on the latter. This picture is translated to a description in terms of Yetter-Drinfeld and Hopf modules over quasi-bialgebras in a braided monoidal category. Via braided reconstruction theory, intrinsic definitions of braided Drinfeld and Heisenberg doubles are obtained, together with a generalization of the result of Lu (1994) that the Heisenberg double is a 2-cocycle twist of the Drinfeld double for general braided Hopf algebras. Chapter 2 : In this chapter, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf algebras which are of what we call weakly separable type, we obtain a class of pointed Hopf algebras which can be viewed as natural generalizations of multiparameter deformations of universal enveloping algebras of Lie algebras. These Hopf algebras are instances of a new version of braided Drinfeld doubles, which we call asymmetric braided Drinfeld doubles. This is a generalization of an earlier result by Benkart and Witherspoon (2004) who showed that two-parameter quantum groups are Drinfeld doubles. It is possible to recover a Lie algebra from these doubles in the case where the group is free and the parameters are generic. The Lie algebras arising are generated by Lie subalgebras isomorphic to sl2. Chapter 3 : The universal enveloping algebra U(trn) of a Lie algebra associated to the classical Yang-Baxter equation was introduced in 2006 by Bartholdi-Enriquez-Etingof-Rains where it was shown to be Koszul. This algebra appears as the An-1 case in a general class of braided Hopf algebras in work of Bazlov-Berenstein (2009) for any complex reection group. In this chapter, we show that the algebras corresponding to the series Bn and Dn, which are again universal enveloping algebras, are Koszul. This is done by constructing a PBW-basis for the quadratic dual. We further show how results of Bazlov-Berenstein can be used to produce pairs of adjoint functors between categories of rational Cherednik algebra representations of different rank and type for the classical series of Coxeter groups. Chapter 4 : Quantum groups can be understood as braided Drinfeld doubles over the group algebra of a lattice. The main objects of this chapter are certain braided Drinfeld doubles over the Drinfeld double of an irreducible complex reflection group. We argue that these algebras are analogues of the Drinfeld-Jimbo quantum enveloping algebras in a setting relevant for rational Cherednik algebra. This analogy manifests itself in terms of categorical actions, related to the general Drinfeld-Heisenberg double picture developed in Chapter 2, using embeddings of Bazlov and Berenstein (2009). In particular, this work provides a class of quasitriangular Hopf algebras associated to any complex reflection group which are in some cases finite-dimensional.
17
Haydon, James Henri. "Étale homotopy sections of algebraic varieties." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:88019ba2-a589-4179-ad7f-1eea234d284c.
Full textAbstract:
We define and study the fundamental pro-finite 2-groupoid of varieties X defined over a field k. This is a higher algebraic invariant of a scheme X, analogous to the higher fundamental path 2-groupoids as defined for topological spaces. This invariant is related to previously defined invariants, for example the absolute Galois group of a field, and Grothendieck’s étale fundamental group. The special case of Brauer-Severi varieties is considered, in which case a “sections conjecture” type theorem is proved. It is shown that a Brauer-Severi variety X has a rational point if and only if its étale fundamental 2-groupoid has a special sort of section.
18
Simons, Nicholas James. "The width of verbal subgroups in profinite groups." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:01075c36-c7e6-4def-9647-86b4346e4726.
Full textAbstract:
The main result of this thesis is an original proof that every word has finite width in a compact $p$-adic analytic group. The proof we give here is an alternative to Andrei Jaikin-Zapirain's recent proof of the same result, and utilises entirely group-theoretical ideas. We accomplish this by reducing the problem to a proof that every word has finite width in a profinite group which is virtually a polycyclic pro-$p$ group. To obtain this latter result we first establish that such a group can be embedded as an open subgroup of a group of the form $N_1M_1$, where $N_1$ is a finitely generated closed normal nilpotent subgroup, and $M_1$ is a finitely generated closed nilpotent-by-finite subgroup; we then adapt a method of V. A. Romankov. As a corollary we note that our approach also proves that every word has finite width in a polycyclic-by-finite group (which is not profinite). As a supplementary result we show that for finitely generated closed subgroups $H$ and $K$ of a profinite group the commutator subgroup $[H,K]$ is closed, and give examples to show that various hypotheses are necessary. This implies that the outer-commutator words have finite width in profinite groups of finite rank. We go on to establish some bounds for this width. In addition, we show that every word has finite width in a product of a nilpotent group of finite rank and a virtually nilpotent group of finite rank. We consider the possible application of this to soluble minimax groups.
19
Wade, Richard D. "Symmetries of free and right-angled Artin groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:b856e2b5-3689-472b-95c1-71b5748affc9.
Full textAbstract:
The objects of study in this thesis are automorphism groups of free and right-angled Artin groups. Right-angled Artin groups are defined by a presentation where the only relations are commutators of the generating elements. When there are no relations the right-angled-Artin group is a free group and if we take all possible relations we have a free abelian group. We show that if no finite index subgroup of a group $G$ contains a normal subgroup that maps onto $mathbb{Z}$, then every homomorphism from $G$ to the outer automorphism group of a free group has finite image. The above criterion is satisfied by SL$_m(mathbb{Z})$ for $m geq 3$ and, more generally, all irreducible lattices in higher-rank, semisimple Lie groups with finite centre. Given a right-angled Artin group $A_Gamma$ we find an integer $n$, which may be easily read off from the presentation of $A_G$, such that if $m geq 3$ then SL$_m(mathbb{Z})$ is a subgroup of the outer automorphism group of $A_Gamma$ if and only if $m leq n$. More generally, we find criteria to prevent a group from having a homomorphism to the outer automorphism group of $A_Gamma$ with infinite image, and apply this to a large number of irreducible lattices as above. We study the subgroup $IA(A_Gamma)$ of $Aut(A_Gamma)$ that acts trivially on the abelianisation of $A_Gamma$. We show that $IA(A_Gamma)$ is residually torsion-free nilpotent and describe its abelianisation. This is complemented by a survey of previous results concerning the lower central series of $A_Gamma$. One of the commonly used generating sets of $Aut(F_n)$ is the set of Whitehead automorphisms. We describe a geometric method for decomposing an element of $Aut(F_n)$ as a product of Whitehead automorphisms via Stallings' folds. We finish with a brief discussion of the action of $Out(F_n)$ on Culler and Vogtmann's Outer Space. In particular we describe translation lengths of elements with regards to the `non-symmetric Lipschitz metric' on Outer Space.
20
Garrido, Alejandra. "Aspects of branch groups." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:79a3e094-38ac-424b-a83d-abb26257bfd2.
Full textAbstract:
This thesis is a study of the subgroup structure of some remarkable groups of automorphisms of rooted trees. It is divided into two parts. The main result of the first part is seemingly of an algorithmic nature, establishing that the Gupta--Sidki 3-group G has solvable membership problem. This follows the approach of Grigorchuk and Wilson who showed the same result for the Grigorchuk group. The proof, however, is not algorithmic, and it moreover shows a striking subgroup property of G: that all its infinite finitely generated subgroups are abstractly commensurable with either G or G × G. This is then used to show that G is subgroup separable which, together with some nice presentability properties of G, implies that the membership problem is solvable. The proof of the main theorem is also used to show that G satisfies a "strong fractal" property, in that every infinite finitely generated subgroup acts like G on some rooted subtree. The second part concerns the subgroup structure of branch and weakly branch groups in general. Motivated by a natural question raised in the first part, a necessary condition for direct products of branch groups to be abstractly commensurable is obtained. From this condition it follows that the Gupta--Sidki 3-group is not abstractly commensurable with its direct square. The first main result in the second part states that any (weakly) branch action of a group on a rooted tree is determined by the subgroup structure of the group. This is then applied to answer a question of Bartholdi, Siegenthaler and Zalesskii, showing that the congruence subgroup property for branch and weakly branch groups is independent of the actions on a tree. Finally, the information obtained on subgroups of branch groups is used to examine which groups have an essentially unique branch action and why this holds.
21
Cooney, Nicholas. "Quantum multiplicative hypertoric varieties and localization." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:17d0824f-e8f2-4cb7-9e84-dd3850a9e2a2.
Full textAbstract:
In this thesis, we consider q-deformations of multiplicative Hypertoric varieties, where q∈𝕂x for 𝕂 an algebraically closed field of characteristic 0. We construct an algebra Dq of q-difference operators as a Heisenberg double in a braided monoidal category. We then focus on the case where q is specialized to a root of unity. In this setting, we use Dq to construct an Azumaya algebra on an l-twist of the multiplicative Hypertoric variety, before showing that this algebra splits over the fibers of both the moment and resolution maps. Finally, we sketch a derived localization theorem for these Azumaya algebras.
22
Thomas, Teri M. "A Generalization of Sylow’s Theorem." Youngstown State University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1256911896.
Full text
23
Thomas, Teri M. "A generalization of Sylow's theorem /." Connect to resource online, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1256911896.
Full text
24
Hofmann, Natalie. "Hill's theorem of formal groups : applications, generalizations and counterexamples." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=68183.
Full textAbstract:
One-dimensional formal groups were classified by W. Hill who showed in particular that one-dimensional formal groups are isomorphic over p-adic integers if and only if they have the same associated Eisenstein polynomial. This result can be applied to show that the torsion points on any supersingular elliptic curve over the field of p-adic numbers generate abelian extensions of the unramified quadradic extension of the field. The theorem cannot be extended to classify formal groups of higher dimension. Counterexamples will be provided both in the case of two-dimensional formal groups and when the formal group is defined over an extension of the p-adic integers. Constructions and classifications of higher dimensional formal groups due to T. Nakamura and M. Hazewinkel will also be explored.
25
Compton, D'Lane Rebecca. "The generation and effects of a stigma in small groups: a formal theory and test." Texas A&M University, 2007. http://hdl.handle.net/1969.1/85881.
Full textAbstract:
Drawing from the vast literature on stigmas, theories of status generalizations
and affect, this study employs a formal framework to delineate among different kinds of
stigmas and different processes by which they might operate. This study then considers
the case of a particular type of stigma, a behavioral stigma, a label that is obtained from
past behavior. The formalization distinguishes how knowledge of a particular type of
stigma operates through group members who then cast an â otherâ into a stigmatized role
with special attention to affect and behavior of the stigmatized individual and the other
group members. Additionally, I am able to study the developmental process of stigma
because, in the particular theoretical case I consider, the stigmatized individual is
initially unaware of the stigma.
The findings indicate that stigma were created and did have an effect on
individuals and groups. While the observable power and prestige effects were much
more pronounced for measures of content versus measures of amount of interaction stigmatized groups were characterized by more disapproval, fewer agreements and more
interruptions than were nonstigmatized groups. Further, those who were stigmatized had
less influence than other group members. In terms of feelings, there was support for the
hypotheses suggesting that stigmatized individuals rate both themselves and their groups
more negatively than do nonstigmatized group members. Also, those who were not
stigmatized rated the stigmatized person more negatively than others. While there were
no significant differences between Stigmatized and Control groups relative to happiness
or group cohesion and efficiency, those in the Control groups were more committed to
their groups than were those in the Stigmatized groups.
This study contributes to the large literature on stigma by examining one kind of
stigma. It also contributes to several established literatures in social psychological
theory. This study has implications for the power of the social construction of stigma
and consequently for the power of social construction in the dismantling of stigma.
26
Li, Bishan. "Generalizations of diagonal dominance in matrix theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ30262.pdf.
Full text
27
Wai, Hon-kit. "Two Generalizations of Witten-Helffer-Sjöstrand Theory /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487929230739623.
Full text
28
Schmid, Dominik. "Scattered data approximation on the rotation group and generalizations." Aachen Shaker, 2009. http://d-nb.info/995021562/04.
Full text
29
Ko, Hong Fu. "Marcinkiewicz's theorem and its generalizations /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20KO.
Full text
30
McCall, Kevin J. "3-Maps And Their Generalizations." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5581.
Full textAbstract:
A 3-map is a 3-region colorable map. They have been studied by Craft and White in their paper 3-maps. This thesis introduces topological graph theory and then investigates 3-maps in detail, including examples, special types of 3-maps, the use of 3-maps to find the genus of special graphs, and a generalization known as n-maps.
31
Avventi, Enrico. "Spectral Moment Problems : Generalizations, Implementation and Tuning." Doctoral thesis, KTH, Optimeringslära och systemteori, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-39026.
Full textAbstract:
Spectral moment interpolation find application in a wide array of use cases: robust control, system identification, model reduction to name the most notable ones. This thesis aims to expand the theory of such methods in three different directions. The first main contribution concerns the practical applicability. From this point of view various solving algorithm and their properties are considered. This study lead to identify a globally convergent method with excellent numerical properties. The second main contribution is the introduction of an extended interpolation problem that allows to model ARMA spectra without any explicit information of zero’s positions. To this end it was necessary for practical reasons to consider an approximated interpolation insted. Finally, the third main contribution is the application to some problems such as graphical model identification and ARMA spectral approximation.QC 20110906
32
Kieburg, Mario [Verfasser]. "Chiral Random Matrix Theory: Generalizations and Applications / Mario Kieburg." Bielefeld : Universitätsbibliothek Bielefeld, 2015. http://d-nb.info/1074999053/34.
Full text
33
Abbas, Mujahid. "Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications." Doctoral thesis, Universitat Politècnica de València, 2015. http://hdl.handle.net/10251/48470.
Full textAbstract:
Mathematical models have extensively been used in problems related to
engineering, computer sciences, economics, social, natural and medical sciences
etc. It has become very common to use mathematical tools to solve,
study the behavior and different aspects of a system and its different subsystems.
Because of various uncertainties arising in real world situations,
methods of classical mathematics may not be successfully applied to solve
them. Thus, new mathematical theories such as probability theory and fuzzy
set theory have been introduced by mathematicians and computer scientists
to handle the problems associated with the uncertainties of a model. But
there are certain deficiencies pertaining to the parametrization in fuzzy set
theory. Soft set theory aims to provide enough tools in the form of parameters
to deal with the uncertainty in a data and to represent it in a useful
way. The distinguishing attribute of soft set theory is that unlike probability
theory and fuzzy set theory, it does not uphold a precise quantity. This
attribute has facilitated applications in decision making, demand analysis,
forecasting, information sciences, mathematics and other disciplines.
In this thesis we will discuss several algebraic and topological properties
of soft sets and fuzzy soft sets. Since soft sets can be considered as setvalued
maps, the study of fixed point theory for multivalued maps on soft
topological spaces and on other related structures will be also explored.
The contributions of the study carried out in this thesis can be summarized
as follows:
i) Revisit of basic operations in soft set theory and proving some new
results based on these modifications which would certainly set a new
dimension to explore this theory further and would help to extend its
limits further in different directions. Our findings can be applied to
develop and modify the existing literature on soft topological spaces
ii) Defining some new classes of mappings and then proving the existence
and uniqueness of such mappings which can be viewed as a positive
contribution towards an advancement of metric fixed point theory
iii) Initiative of soft fixed point theory in framework of soft metric spaces
and proving the results lying at the intersection of soft set theory and
fixed point theory which would help in establishing a bridge between
these two flourishing areas of research.
iv) This study is also a starting point for the future research in the area of
fuzzy soft fixed point theory.Abbas, M. (2014). Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48470
TESIS
34
Kissel, Kris. "Generalizations of a result of Lewis and Vogel /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/5741.
Full text
35
Schmid, Dominik [Verfasser]. "Scattered Data Approximation on the Rotation Group and Generalizations / Dominik Schmid." Aachen : Shaker, 2009. http://d-nb.info/1161303006/34.
Full text
36
Tse, Chun, and 謝進. "Some generalizations on the problem of non-Goldbach numbers." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31225238.
Full text
37
Rasnick, Rebecca. "Generalizations of the Arcsine Distribution." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3565.
Full textAbstract:
The arcsine distribution looks at the fraction of time one player is winning in a fair coin toss game and has been studied for over a hundred years. There has been little further work on how the distribution changes when the coin tosses are not fair or when a player has already won the initial coin tosses or, equivalently, starts with a lead. This thesis will first cover a proof of the arcsine distribution. Then, we explore how the distribution changes when the coin the is unfair. Finally, we will explore the distribution when one person has won the first few flips.
38
Schmid, Bernhard [Verfasser]. "Mode-coupling theory: generalizations, high dimensions and microscopic dynamics / Bernhard Schmid." Mainz : Universitätsbibliothek Mainz, 2011. http://d-nb.info/1026802563/34.
Full text
39
Blizard, W. D. "Generalizations of the concept of set : a formal theory of multisets." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370239.
Full text
40
Nearing, Grey Stephen. "Diagnostics and Generalizations for Parametric State Estimation." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293533.
Full textAbstract:
This dissertation is comprised of a collection of five distinct research projects which apply, evaluate and extend common methods for land surface data assimilation. The introduction of novel diagnostics and extensions of existing algorithms is motivated by an example, related to estimating agricultural productivity, of failed application of current methods. We subsequently develop methods, based on Shannon's theory of communication, to quantify the contributions from all possible factors to the residual uncertainty in state estimates after data assimilation, and to measure the amount of information contained in observations which is lost due to erroneous assumptions in the assimilation algorithm. Additionally, we discuss an appropriate interpretation of Shannon information which allows us to measure the amount of information contained in a model, and use this interpretation to measure the amount of information introduced during data assimilation-based system identification. Finally, we propose a generalization of the ensemble Kalman filter designed to alleviate one of the primary assumptions - that the observation function is linear.
41
Garrod, Bryn James. "Problems of optimal choice on posets and generalizations of acyclic colourings." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/243496.
Full textAbstract:
This dissertation is in two parts, each of three chapters. In Part 1, I shall prove some results concerning variants of the 'secretary problem'. In Part 2, I shall bound several generalizations of the acyclic chromatic number of a graph as functions of its maximum degree. I shall begin Chapter 1 by describing the classical secretary problem, in which the aim is to select the best candidate for the post of a secretary, and its solution. I shall then summarize some of its many generalizations that have been studied up to now, provide some basic theory, and briefly outline the results that I shall prove. In Chapter 2, I shall suppose that the candidates come as ‘m’ pairs of equally qualified identical twins. I shall describe an optimal strategy, a formula for its probability of success and the asymptotic behaviour of this strategy and its probability of success as m → ∞. I shall also find an optimal strategy and its probability of success for the analagous version with ‘c’-tuplets. I shall move away from known posets in Chapter 3, assuming instead that the candidates come from a poset about which the only information known is its size and number of maximal elements. I shall show that, given this information, there is an algorithm that is successful with probability at least ¹/e . For posets with ‘k ≥ 2’ maximal elements, I shall prove that if their width is also ‘k’ then this can be improved to ‘k-1√1/k’ and show that no better bound of this type is possible. In Chapter 4, I shall describe the history of acyclic colourings, in which a graph must be properly coloured with no two-coloured cycle, and state some results known about them and their variants. In particular, I shall highlight a result of Alon, McDiarmid and Reed, which bounds the acyclic chromatic number of a graph by a function of its maximum degree. My results in the next two chapters are of this form. I shall consider two natural generalizations in Chapter 5. In the first, only cycles of length at least ’l’ must receive at least three colours. In the second, every cycle must receive at least ‘c’ colours, except those of length less than ‘c’, which must be multicoloured. My results in Chapter 6 generalize the concept of a cycle; it is now subgraphs with minimum degree ‘r’ that must receive at least three colours, rather than subgraphs with minimum degree two (which contain cycles). I shall also consider a natural version of this problem for hypergraphs.
42
Sinitsyn, Nikolai. "Generalizations of the Landau-Zener theory in the physics of nanoscale systems." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/216.
Full textAbstract:
Nanoscale systems have sizes intermediate between atomic and macroscopic ones. Therefore their treatment often requires a combination of methods from atomic and condensed matter physics. The conventional Landau-Zener theory, being a powerful tool in atomic physics, often fails to predict correctly nonadiabatic transition probabilities in various nanostructures because it does not include many-body effects typical for mesoscopics. In this research project the generalizations of the Landau-Zener theory that solve this problem were studied. The multistate, multiparticle and nonunitary extensions of the theory have been proposed and investigated. New classes of exactly solvable models have been derived. I discuss their applications in problems of the molecular condensate dissociation and of the driven charge transport. In application to the physics of nanomagnets new approaches in modeling the influence of the environment on the Landau-Zener evolution are proposed and simple universal formulas are derived for the extensions of the theory that include the coupling to noise and the nuclear spin bath.
43
Hu, Ting. "Convergence of the mean shift algorithm and its generalizations." Master's thesis, University of Central Florida, 2011. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4925.
Full textAbstract:
Mean shift is an effective iterative algorithm widely used in image analysis tasks like tracking, image segmentation, smoothing, filtering, edge detection and etc. It iteratively estimates the modes of the probability function of a set of sample data points based in a region. Mean shift was invented in 1975, but it was not widely used until the work by Cheng in 1995. After that, it becomes popular in computer vision. However the convergence, a key character of any iterative algorithm, has been rigorously proved only very recently, but with strong assumptions. In this thesis, the method of mean shift is introduced systematically first and then the convergence is established under more relaxed assumptions. Finally, generalization of the mean shift method is also given for the estimation of probability density function using generalized multivariate smoothing functions to meet the need for more real life applications.ID: 030423142; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Error in paging: p. vi followed by one unnumbered page followed by p. ii-iv.; Thesis (M.S.)--University of Central Florida, 2011.; Includes bibliographical references (p. 61-62).
M.S.
Masters
Mathematics
Sciences
44
Martin, Michael Patrick McAlarnen. "Computational Group Theory." Thesis, The University of Arizona, 2015. http://hdl.handle.net/10150/579297.
Full textAbstract:
The study of finite groups has been the subject of much research, with substantial success in the 20th century, in part due to the development of representation theory. Representation theory allows groups to be studied using the well-understood properties of linear algebra, however it requires the researcher to supply a representation of the group. One way to produce representations of groups is to take a representation of a subgroup and use it to induce a representation. We focus on the finite simple groups because they are the buliding blocks of an arbitrary simple group. This thesis investigates an algorithm to induce representations of large finite simple groups from a representation of a subgroup.
45
Niyitegeka, Jean Marie Vianney. "Generalizations of some fixed point theorems in banach and metric spaces." Thesis, Nelson Mandela Metropolitan University, 2015. http://hdl.handle.net/10948/5265.
Full textAbstract:
A fixed point of a mapping is an element in the domain of the mapping that is mapped into itself by the mapping. The study of fixed points has been a field of interests to mathematicians since the discovery of the Banach contraction theorem, i.e. if is a complete metric space and is a contraction mapping (i.e. there exists such that for all ), then has a unique fixed point. The Banach contraction theorem has found many applications in pure and applied mathematics. Due to fixed point theory being a mixture of analysis, geometry, algebra and topology, its applications to other fields such as physics, economics, game theory, chemistry, engineering and many others has become vital. The theory is nowadays a very active field of research in which many new theorems are published, some of them applied and many others generalized. Motivated by all of this, we give an exposition of some generalizations of fixed point theorems in metric fixed point theory, which is a branch of fixed point theory about results of fixed points of mappings between metric spaces, where certain properties of the mappings involved need not be preserved under equivalent metrics. For instance, the contractive property of mappings between metric spaces need not be preserved under equivalent metrics. Since metric fixed point theory is wide, we limit ourselves to fixed point theorems for self and non-self-mappings on Banach and metric spaces. We also take a look at some open problems on this topic of study. At the end of the dissertation, we suggest our own problems for future research.
46
McSorley, J. P. "Topics in group theory." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376929.
Full text
47
Hegedüs, Pál. "Topics in group theory." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620412.
Full text
48
Colletti, Bruce William. "Group theory and metaheuristics /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.
Full text
49
Kracht, Darci L. "Applications of the Artin-Hasse Exponential Series and Its Generalizations to Finite Algebra Groups." Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1322505829.
Full text
50
Engelke, Sebastian. "Brown-Resnick Processes: Analysis, Inference and Generalizations." Doctoral thesis, Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F1B3-2.
Full text