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Dissertations / Theses on the topic 'Infinite groups : Group theory'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Griffin, Cornelius John. "Subgroups of infinite groups : interactions between group theory and number theory." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252018.

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2

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.

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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 us

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3

Ramsay, Denise. "On linearly ordered sets and permutation groups of uncountable degree." Thesis, University of Oxford, 1990. http://ora.ox.ac.uk/objects/uuid:ce9a8b26-bb4c-4c85-8231-78e89ce4109d.

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In this thesis a set, Ω, of cardinality N<sub>K</sub> and a group acting on Ω, with N<sub>K+1</sub> orbits on the power set of Ω, is found for every infinite cardinal N<sub>K</sub>. Let W<sub>K</sub> denote the initial ordinal of cardinality N<sub>K</sub>. Define N := {α<sub>1</sub>α<sub>2</sub> . . . α<sub>n</sub>∣ 0 < n < w, α<sub>j</sub> ∈ w<sub>K</sub> for j = 1, . . .,n, α<sub>n</sub> a successor ordinal} R := {ϰ ∈ N ∣ length(ϰ) = 1 mod 2} and let these sets be ordered lexicographically. The order types of N and R are Κ-types (countable unions of scattered types) which have cardinality N<

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4

Smith, Simon Mark. "Subdegree growth rates of infinite primitive permutation groups." Thesis, University of Oxford, 2005. http://ora.ox.ac.uk/objects/uuid:1baa0e15-363a-4163-b21b-59fcd62d210b.

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If G is a group acting on a set Ω, and α, β ∈ Ω, the directed graph whose vertex set is Ω and whose edge set is the orbit (α, β)<sup>G</sup> is called an orbital graph of G. These graphs have many uses in permutation group theory. A graph Γ is said to be primitive if its automorphism group acts primitively on its vertex set, and is said to have connectivity one if there is a vertex α such that the graph Γ\{α} is not connected. A half-line in Γ is a one-way infinite path in Γ. The ends of a locally finite graph Γ are equivalence classes on the set of half-lines: two half-lines lie in the same e

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5

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.

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<b>Asymptotic cones.</b> 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

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6

Bernstein, Brett David. "Higher natural numbers and omega words." Diss., Online access via UMI:, 2005.

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7

Hume, David S. "Embeddings of infinite groups into Banach spaces." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde.

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In this thesis we build on the theory concerning the metric geometry of relatively hyperbolic and mapping class groups, especially with respect to the difficulty of embedding such groups into Banach spaces. In Chapter 3 (joint with Alessandro Sisto) we construct simple embeddings of closed graph manifold groups into a product of three metric trees, answering positively a conjecture of Smirnov concerning the Assouad-Nagata dimension of such spaces. Consequently, we obtain optimal embeddings of such spaces into certain Banach spaces. The ideas here have been extended to other closed three-manifo

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8

Olukoya, Feyisayo. "Decision problems in groups of homeomorphisms of Cantor space." Thesis, University of St Andrews, 2018. http://hdl.handle.net/10023/15885.

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The Thompson groups $F, T$ and $V$ are important groups in geometric group theory: $T$ and $V$ being the first discovered examples of finitely presented infinite simple groups. There are many generalisations of these groups including, for $n$ and $r$ natural numbers and $1 < r < n$, the groups $F_{n}$, $T_{n,r}$ and $G_{n,r}$ ($T ≅ T_{2,1}$ and $V ≅ G_{2,1}$). Automorphisms of $F$ and $T$ were characterised in the seminal paper of Brin ([16]) and, later on, Brin and Guzman ([17]) investigate automorphisms of $T_{n, n-1}$ and $F_{n}$ for $n > 2$. However, their techniques give no information ab

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9

Ramras, Daniel A. "Stable representation theory of infinite discrete groups /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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10

Carruth, Nathan Thomas. "Classical Foundations for a Quantum Theory of Time in a Two-Dimensional Spacetime." DigitalCommons@USU, 2010. https://digitalcommons.usu.edu/etd/708.

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We consider the set of all spacelike embeddings of the circle S1 into a spacetime R1 × S1 with a metric globally conformal to the Minkowski metric. We identify this set and the group of conformal isometries of this spacetime as quotients of semidirect products involving diffeomorphism groups and give a transitive action of the conformal group on the set of spacelike embeddings. We provide results showing that the group of conformal isometries is a topological group and that its action on the set of spacelike embeddings is continuous. Finally, we point out some directions for future research.

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11

Takata, Doman. "A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds." Kyoto University, 2018. http://hdl.handle.net/2433/232217.

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12

Qi, Dongwen. "On irreducible, infinite, non-affine coxeter groups." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1185463175.

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13

Maia, LuÃs Farias. "Coberturas de grupos." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5772.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico<br>Esta dissertaÃÃo apresenta resultados sobre coberturas de grupos por sub-grupos abelianos, subgrupos de Sylow e subgrupos normais. O Teorema de Neumann Ã indispensÃvel no estudo das coberturas por subgrupos. Apresentamos no apÃndice C uma prova elementar de um resultado muito importante nas coberturas p-Sylow.<br>The paper results on the Coverage groups by abelian subgroups, subgroups of Sylow and normal subgroups. We present in appendix C an elementary proof a very important result in the coverage p-Sylow.

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14

Emms, Josephine. "Amalgamation classes of directed graphs in model theory and infinite permutation groups." Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/39034/.

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15

Bieniecka, Ewa. "Commutativity and free products in Thompson's Group V." Thesis, University of St Andrews, 2018. http://hdl.handle.net/10023/14652.

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We broaden the theory of dynamical interpretation, investigate the property of commutativity and explore the subject of subgroups forming free products in Thompson's group V. We expand Brin's terminology for a revealing pair to an any tree pair. We use it to analyse the dynamical behaviour of an arbitrary tree pair which cannot occur in a revealing pair. Hence, we design a series of algorithms generating Brin's revealing pair from any tree pair, by successively eliminating the undesirable structures. To detect patterns and transitioning between tree pairs, we introduce a new combinatorial obje

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16

Lima, Francismar Ferreira 1985. "Pontos fixos por grupos finitos agindo sobre grupos solúveis de tipo FP infinito." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306924.

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Orientador: Dessislava Hristova Kochloukova<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-23T11:19:15Z (GMT). No. of bitstreams: 1 Lima_FrancismarFerreira_M.pdf: 2264816 bytes, checksum: 31f3b411247775dcde6338655fbd496b (MD5) Previous issue date: 2013<br>Resumo: O resumo poderá ser visualizado no texto completo da tese digital<br>Abstract: The complete Abstract is available with the full electronic document.<br>Mestrado<br>Matematica<br>Mestre em Matemática

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17

Gavira, Romero Alberto. "Cellular approximations of infinite loop spaces and classifying spaces." Doctoral thesis, Universitat Autònoma de Barcelona, 2014. http://hdl.handle.net/10803/133278.

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Dado un espacio topológico punteado A, E. Dror-Farjoun introduce en 1995 la noción de A-homotopía, donde A y sus suspensiones juegan el mismo papel que las esferas en homotopía clásica. Por tanto se definen los grupos de A-homotopía de un espacio punteado X como las clases de homotopía de aplicaciones definidas desde las suspensiones de A a X. La idea de CW-complejo es sustituida por la de espacio A-celular, i.e., un espacio construido mediante ciertos colímites homotópicos punteados de A de manera iterada. El concepto de aproximación celular es remplazada por la de aproximación A-celular, est

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18

Penrod, Keith G. "Infinite Product Group." BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/976.

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The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.

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19

Dexter, Cache Porter. "Schur Rings over Infinite Groups." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/8831.

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A Schur ring is a subring of the group algebra with a basis that is formed by a partition of the group. These subrings were initially used to study finite permutation groups, and classifications of Schur rings over various finite groups have been studied. Here we investigate Schur rings over various infinite groups, including free groups. We classify Schur rings over the infinite cyclic group.

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20

Crawley-Boevey, W. W. "Polycyclic-by-finite affine group schemes and infinite soluble groups." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372868.

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21

Sutherland, David C. (David Craig). "Automorphism Groups of Strong Bruhat Orders of Coxeter Groups." Thesis, North Texas State University, 1986. https://digital.library.unt.edu/ark:/67531/metadc330906/.

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In this dissertation, we describe the automorphism groups for the strong Bruhat orders A_n-1, B_n, and D_n. In particular, the automorphism group of A_n-1 for n ≥ 3 is isomorphic to the dihedral group of order eight, D_4; the automorphism group of B_n for n ≥ 3 is isomorphic to C_2 x C_2 where C_2 is the cyclic group of order two; the automorphism group of D_n for n > 5 and n even is isomorphic to C_2 x C_2 x C_2; and the automorphism group of D_n for n ≥ 5 and n odd is isomorphic to the dihedral group D_4.

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22

Isenrich, Claudio Llosa. "Kähler groups and Geometric Group Theory." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:4a7ab097-4de5-4b72-8fd6-41ff8861ffae.

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In this thesis we study Kähler groups and their connections to Geometric Group Theory. This work presents substantial progress on three central questions in the field: (1) Which subgroups of direct products of surface groups are Kähler? (2) Which Kähler groups admit a classifying space with finite (n-1)-skeleton but no classifying space with finitely many n-cells? (3) Is it possible to give explicit finite presentations for any of the groups constructed in response to Question 2? Question 1 was raised by Delzant and Gromov. Question 2 is intimately related to Question 1: the non-trivial exa

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23

Taylor, Paul Anthony. "Computational investigation into finite groups." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/computational-investigation-into-finite-groups(8fe69098-a2d0-4717-b8d3-c91785add68c).html.

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We briefly discuss the algorithm given in [Bates, Bundy, Perkins, Rowley, J. Algebra, 316(2):849-868, 2007] for determining the distance between two vertices in a commuting involution graph of a symmetric group.We develop the algorithm in [Bates, Rowley, Arch. Math. (Basel), 85(6):485-489, 2005] for computing a subgroup of the normalizer of a 2-subgroup X in a finite group G, examining in particular the issue of when to terminate the randomized procedure. The resultant algorithm is capable of handling subgroups X of order up to 512 and is suitable, for example, for matrix groups of large degre

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24

Atim, Alexandru Gabriel. "Uniqueness Results for the Infinite Unitary, Orthogonal and Associated Groups." Thesis, University of North Texas, 2008. https://digital.library.unt.edu/ark:/67531/metadc6136/.

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Let H be a separable infinite dimensional complex Hilbert space, let U(H) be the Polish topological group of unitary operators on H, let G be a Polish topological group and φ:G→U(H) an algebraic isomorphism. Then φ is a topological isomorphism. The same theorem holds for the projective unitary group, for the group of *-automorphisms of L(H) and for the complex isometry group. If H is a separable real Hilbert space with dim(H)≥3, the theorem is also true for the orthogonal group O(H), for the projective orthogonal group and for the real isometry group. The theorem fails for U(H) if H is finite

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25

Coutts, Hannah Jane. "Topics in computational group theory : primitive permutation groups and matrix group normalisers." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2561.

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Part I of this thesis presents methods for finding the primitive permutation groups of degree d, where 2500 ≤ d < 4096, using the O'Nan-Scott Theorem and Aschbacher's theorem. Tables of the groups G are given for each O'Nan-Scott class. For the non-affine groups, additional information is given: the degree d of G, the shape of a stabiliser in G of the primitive action, the shape of the normaliser N in S[subscript(d)] of G and the rank of N. Part II presents a new algorithm NormaliserGL for computing the normaliser in GL[subscript(n)](q) of a group G ≤ GL[subscript(n)](q). The algorithm is impl

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26

Möller, Rögnvaldur G. "Groups acting on graphs." Thesis, University of Oxford, 1991. http://ora.ox.ac.uk/objects/uuid:2dacfc67-56c4-4541-b52e-10199a13dcc2.

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In the first part of this thesis we investigate the automorphism groups of regular trees. In the second part we look at the action of the automorphism group of a locally finite graph on the ends of the graph. The two part are not directly related but trees play a fundamental role in both parts. Let T<sub>n</sub> be the regular tree of valency n. Put G := Aut(T<sub>n</sub>) and let G<sub>0</sub> be the subgroup of G that is generated by the stabilisers of points. The main results of the first part are : Theorem 4.1 Suppose 3 ≤ n < N<sub>0</sub> and α ϵ T<sub>n</sub>. Then G<sub>α</sub> (the sta

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27

Hardy, Philip David. "Aspects of abstract and profinite group theory." Thesis, University of Birmingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269887.

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This thesis is in two parts. The first is a study of soluble profinite groups with the maximal condition (max) and mirrors the development of the fundamental properties of polycyclic groups. Two of the main results are a profinite version of Hall's criterion for nilpotence and the existence of nilpotent almost-supplements for the Fitting subgroup. It is shown that the automorphism group of a soluble profinite group with max itself has max and that a soluble profinite group has max if and only if each of its subnormal subgroups of defect at most 2 has max. Quantitative versions of these results

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Mehanna, M. A.-H. "Some computational problems in group theory." Thesis, University of Liverpool, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384569.

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29

Carette, Mathieu. "The automorphism group of accessible groups and the rank of Coxeter groups." Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210261.

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Cette thèse est consacrée à l'étude du groupe d'automorphismes de groupes agissant sur des arbres d'une part, et du rang des groupes de Coxeter d'autre part.<p><p>Via la théorie de Bass-Serre, un groupe agissant sur un arbre est doté d'une structure algébrique particulière, généralisant produits amalgamés et extensions HNN. Le groupe est en fait déterminé par certaines données combinatoires découlant de cette action, appelées graphes de groupes. <p><p>Un cas particulier de cette situation est celle d'un produit libre. Une présentation du groupe d'automorphisme d'un produit libre d'un nombre fi

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30

Astles, David Christopher. "Permutation groups acting on subsets." Thesis, University of East Anglia, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280040.

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31

Makarfi, U. M. "A class of A-groups." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355912.

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32

Bajpai, Jitendra. "Omnipotence of surface groups." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=100245.

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Roughly speaking, a group G is omnipotent if orders of finitely many elements can be controlled independently in some finite quotients of G. We proved that pi1(S) is omnipotent when S is a surface other than P2,T2 or K2 . This generalizes the fact, previously known, that free groups are omnipotent. The proofs primarily utilize geometric techniques involving graphs of spaces with the aim of retracting certain spaces onto graphs.<br>Approximativement, on peut dire qu'un groupe G est omnipotent si les ordresquantité d'élements d'une quantite finie d'elements peuvent etre controles independamment

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33

Lauer, Joseph. "Cubulating one-relator groups with torsion." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101861.

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Let <a1,..., a m | wn> be a presentation of a group G, where w is freely and cyclically reduced and n ≥ 2 is maximal. We define a system of codimension-1 subspaces in the universal cover, and invoke a construction essentially due to Sageev to define an action of G on a CAT(0) cube complex. By proving easily formulated geometric properties of the codimension-1 subspaces we show that when n ≥ 4 the action is proper and cocompact, and that the cube complex is finite dimensional and locally finite. We also prove partial results when n = 2 or n = 3. It is also shown that the subgroups of G generate

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34

Peterson, Aaron. "Pipe diagrams for Thompson's Group F /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1959.pdf.

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35

McHugh, John. "Monomial Characters of Finite Groups." ScholarWorks @ UVM, 2016. http://scholarworks.uvm.edu/graddis/572.

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An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters – those induced from a linear character of some subgroup – since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the class of M-groups, those groups all of whose irreducible characters are monomial. A classical theorem of Taketa asserts that an M-group is necessarily solvable, and Dade proved that every solvable group ca

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36

Smith, Jeremy Francis. "Topics in products of nilpotent groups." Thesis, University of Warwick, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340502.

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Marshall, Joseph. "Computation in hyperbolic groups." Thesis, University of Warwick, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369403.

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Holik, Nicklos L. III. "NONSTANDARD HULLS OF GROUPS." University of Akron / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1176409770.

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Blackburn, Simon R. "Group enumeration." Thesis, University of Oxford, 1992. http://ora.ox.ac.uk/objects/uuid:caac5ed0-44e3-4bec-a97e-59e11ea268af.

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The thesis centres around two problems in the enumeration of p-groups. Define f<sub>φ</sub>(p<sup>m</sup>) to be the number of (isomorphism classes of) groups of order p<sup>m</sup> in an isoclinism class φ. We give bounds for this function as φ is fixed and m varies and as m is fixed and φ varies. In the course of obtaining these bounds, we prove the following result. We say a group is reduced if it has no non-trivial abelian direct factors. Then the rank of the centre Z(P) and the rank of the derived factor group P|P' of a reduced p-group P are bounded in terms of the orders of P|Z(P)P' and

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Menezes, Nina E. "Random generation and chief length of finite groups." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3578.

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Part I of this thesis studies P[subscript(G)](d), the probability of generating a nonabelian simple group G with d randomly chosen elements, and extends this idea to consider the conditional probability P[subscript(G,Soc(G))](d), the probability of generating an almost simple group G by d randomly chosen elements, given that they project onto a generating set of G/Soc(G). In particular we show that for a 2-generated almost simple group, P[subscript(G,Soc(G))](2) 53≥90, with equality if and only if G = A₆ or S₆. Furthermore P[subscript(G,Soc(G))](2) 9≥10 except for 30 almost simple groups G, an

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Bamblett, Jane Carswell. "Algorithms for computing in finite groups." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240616.

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42

Oberholzer, Ria M. "On subnormal subgroups in factorized groups." Thesis, Stellenbosch : Stellenbosch University, 2004. http://hdl.handle.net/10019.1/50050.

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Thesis (MSc) -- Stellenbosch University, 2004.<br>ENGLISH ABSTRACT: In this thesis we give a survey of research done on a problem on subnormal subgroups in factorized groups G = AB, where A and B are two subgroups of G with H a subgroup of A n B which is subnormal in both A and B. It is of interest to know whether or not such a subgroup H will also be subnormal in G. During the past twenty five to thirty years some positive results were obtained in the case where G is a finite group. This was mainly due to work done by Maier and Wielandt, with results by Sidki and Casolo following shortl

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Miyazaki, Takunari. "Polynomial-time computation in matrix groups /." view abstract or download file of text, 2000. http://wwwlib.umi.com/cr/uoregon/fullcit?p9955920.

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Thesis (Ph. D.)--University of Oregon, 2000.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 89-93). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9955920.

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44

Van, Willigenburg Stephanie. "The descent algebras of Coxeter groups." Thesis, University of St Andrews, 1997. http://hdl.handle.net/10023/13713.

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A descent algebra is a subalgebra of the group algebra of a Coxeter group. They were first defined over a field of characteristic zero. In this thesis, the main areas of research to be addressed are; 1. The formulation of a rule for multiplying two elements of descent algebra of the Coxeter groups of type D. 2. The identification of properties exhibited by descent algebras over a field of prime characteristic. In addressing the first, a framework which exploits the specific properties of Coxeter groups is set up. With this framework, a new justification is given for existing rules for multiply

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Brookes, Melanie. "On the efficiency of finite groups." Thesis, University of St Andrews, 1996. http://hdl.handle.net/10023/13682.

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In Chapter 2 of this thesis we look at methods for finding efficient presentations of the transitive permutation groups of degree ≤ 12. Chapter 3 gives efficient presentations for certain direct products of groups including PSL(2, P)2 SL(2, p) X SL(2, 8), PSL(2, p) x C2, for prime p ≥ 5 and PSL(2, 25)3. Chapter 4 introduces a new class of inefficient groups and Chapter 5 gives a brief survey of some of the open problems relating to the efficiency of finite groups.

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Sewell, Cynthia M. (Cynthia Marie). "The Eulerian Functions of Cyclic Groups, Dihedral Groups, and P-Groups." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc500684/.

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Abstract:

In 1935, Philip Hall developed a formula for finding the number of ways of generating the group of symmetries of the icosahedron from a given number of its elements. In doing so, he defined a generalized Eulerian function. This thesis uses Hall's generalized Eulerian function to calculate generalized Eulerian functions for specific groups, namely: cyclic groups, dihedral groups, and p- groups.

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47

邵慰慈 and Wai-chee Shiu. "Schur rings over dihedral groups of order 2p." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1989. http://hub.hku.hk/bib/B31208873.

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48

Shiu, Wai-chee. "Schur rings over dihedral groups of order 2p /." [Hong Kong : University of Hong Kong], 1989. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12364770.

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49

Gill, C. P. "Growth series of certain groups." Thesis, University of Nottingham, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282568.

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50

Moore, Monty L. "On Groups of Positive Type." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc277804/.

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Abstract:

We describe groups of positive type and prove that a group G is of positive type if and only if G admits a non-trivial partition. We completely classify groups of type 2, and present examples of other groups of positive type as well as groups of type zero.

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