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Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Cox, Charles. "Infinite permutation groups containing all finitary permutations." Thesis, University of Southampton, 2016. https://eprints.soton.ac.uk/401538/.

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Groups naturally occu as the symmetries of an object. This is why they appear in so many different areas of mathematics. For example we find class grops in number theory, fundamental groups in topology, and amenable groups in analysis. In this thesis we will use techniques and approaches from various fields in order to study groups. This is a 'three paper' thesis, meaning that the main body of the document is made up of three papers. The first two of these look at permutation groups which contain all permutations with finite support, the first focussing on decision problems and the second on t

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2

Hyatt, Matthew. "Quasisymmetric Functions and Permutation Statistics for Coxeter Groups and Wreath Product Groups." Scholarly Repository, 2011. http://scholarlyrepository.miami.edu/oa_dissertations/609.

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Eulerian quasisymmetric functions were introduced by Shareshian and Wachs in order to obtain a q-analog of Euler's exponential generating function formula for the Eulerian polynomials. They are defined via the symmetric group, and applying the stable and nonstable principal specializations yields formulas for joint distributions of permutation statistics. We consider the wreath product of the cyclic group with the symmetric group, also known as the group of colored permutations. We use this group to introduce colored Eulerian quasisymmetric functions, which are a generalization of Eulerian qua

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3

Kuzucuoglu, M. "Barely transitive permutation groups." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233097.

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4

Lajeunesse, Lisa (Lisa Marie) Carleton University Dissertation Mathematics and Statistics. "Models and permutation groups." Ottawa, 1996.

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5

Schaefer, Artur. "Synchronizing permutation groups and graph endomorphisms." Thesis, University of St Andrews, 2016. http://hdl.handle.net/10023/9912.

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The current thesis is focused on synchronizing permutation groups and on graph endo- morphisms. Applying the implicit classification of rank 3 groups, we provide a bound on synchronizing ranks of rank 3 groups, at first. Then, we determine the singular graph endomorphisms of the Hamming graph and related graphs, count Latin hypercuboids of class r, establish their relation to mixed MDS codes, investigate G-decompositions of (non)-synchronizing semigroups, and analyse the kernel graph construction used in the theorem of Cameron and Kazanidis which identifies non-synchronizing transformations wi

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6

Fawcett, Joanna Bethia. "Bases of primitive permutation groups." Thesis, University of Cambridge, 2013. https://www.repository.cam.ac.uk/handle/1810/252304.

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7

Spiga, Pablo. "P elements in permutation groups." Thesis, Queen Mary, University of London, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.413152.

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8

McNab, C. A. "Some problems in permutation groups." Thesis, University of Oxford, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382633.

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9

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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10

Yang, Keyan. "On Orbit Equivalent Permutation Groups." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1222455916.

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11

Walton, Jacqueline. "Representing the quotient groups of a finite permutation group." Thesis, University of Warwick, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340088.

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12

Xu, Jing. "On closures of finite permutation groups /." Connect to this title, 2005. http://theses.library.uwa.edu.au/adt-WU2006.0023.

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13

Xu, Jing. "On closures of finite permutation groups." University of Western Australia. School of Mathematics and Statistics, 2006. http://theses.library.uwa.edu.au/adt-WU2006.0023.

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[Formulae and special characters in this field can only be approximated. See PDF version for accurate reproduction] In this thesis we investigate the properties of k-closures of certain finite permutation groups. Given a permutation group G on a finite set Ω, for k ≥ 1, the k-closure G(k) of G is the largest subgroup of Sym(Ω) with the same orbits as G on the set Ωk of k-tuples from Ω. The first problem in this thesis is to study the 3-closures of affine permutation groups. In 1992, Praeger and Saxl showed if G is a finite primitive group and k ≥ 2 then either G(k) and G have the same so

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14

Cernes, John. "Ends of permutation groups and some centrality properties of permutational wreath products." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339282.

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15

Maroti, Attila. "Permutation groups and representation theoretic invariants." Thesis, University of Birmingham, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403013.

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16

Benjamin, Ian Francis. "Quasi-permutation representations of finite groups." Thesis, University of Liverpool, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250561.

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17

Tracey, Gareth M. "Minimal generation of transitive permutation groups." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/97251/.

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This thesis discusses upper bounds on the minimal number of elements d(G) required to generate a finite group G. We derive explicit upper bounds for the function d on transitive and minimally transitive permutation groups, in terms of their degree n. In the transitive case, bounds obtained first by Kovács and Newman, then by Bryant, Kovács and Robinson, and finally by Lucchini, Menegazzo and Morigi, show that d(G) = O(n/ √log n), for a transitive permutation group G of degree n. In this thesis, we find best possible estimates for the constant involved.

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18

Sheikh, Atiqa. "Orbital diameters of primitive permutation groups." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/58869.

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Let G be a transitive permutation group acting on a finite set X. Recall that G is primitive if there are no non-trivial equivalence relations on X which are preserved by G. An orbital graph of G is a graph with vertex set X and edges {x,y}, where (x,y) belongs to a fixed orbit of the natural action of G on the set X x X. A well-known result by D.G. Higman asserts that G is primitive if and only if all the orbital graphs are connected. For a primitive group G, we define the orbital diameter of G to be the maximum of the diameters of all orbital graphs of G. Let C be an infinite class of finite

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19

Fiddes, Ceridwyn. "The cyclizer function on permutation groups." Thesis, University of Bath, 2003. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.425697.

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20

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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21

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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22

Vauhkonen, Antti Kalervo. "Finite primitive permutation groups of rank 4." Thesis, Imperial College London, 1993. http://hdl.handle.net/10044/1/58543.

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In this thesis we classify finite primitive permutation groups of rank 4. According to the 0' Nan-Scott theorem, a finite primitive permutation group is an affine group, an almost simple group, or has either simple diagonal action, product action or twisted wreath action. In Chapter 1 we completely determine the primitive rank 4 permutation groups with one of the last three types of actions up to permutation equivalence. In Chapter 2 we use Aschbacher's subgroup structure theorem for the finite classical groups to reduce the classification of affine primitive rank 4 permutation groups G of deg

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23

Turner, Simon. "The cyclizer series of infinite permutation groups." Thesis, University of Bath, 2013. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.577751.

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The cyclizer of an infinite permutation group G is the group generated by the cycles involved in elements of G, along with G itself. There is an ascending subgroup series beginning with G, where each term in the series is the cyclizer of the previous term. We call this series the cyclizer series for G. If this series terminates then we say the cyclizer length of G is the length of the respective cyclizer series. We study several innite permutation groups, and either determine their cyclizer series, or determine that the cyclizer series terminates and give the cyclizer length. In each of the in

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24

Mazhar, Siddiqua. "Composition of permutation representations of triangle groups." Thesis, University of Newcastle upon Tyne, 2017. http://hdl.handle.net/10443/3857.

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A triangle group is denoted by (p, q, r) and has finite presentation (p, q, r) = hx, y|xp = yq = (xy)r = 1i. In the 1960’s Higman conjectured that almost every triangle group has among its homomorphic images all but finitely many of the alternating groups. This was proved by Everitt in [6]. In this thesis, we combine permutation representations using the methods used in the proof of Higman’s conjecture. We do some experiments by using GAP code and then we examine the situations where the composition of a number of coset diagrams for a triangle group is imprimitive. Chapter 1 provides the intro

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25

Hendriksen, Michael Arent. "Minimal Permutation Representations of Classes of Semidirect Products of Groups." Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/14353.

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Given a finite group $G$, the smallest $n$ such that $G$ embeds into the symmetric group $S_n$ is referred to as the minimal degree. Much of the accumulated literature focuses on the interplay between minimal degrees and direct products. This thesis extends this to cover large classes of semidirect products. Chapter 1 provides a background for minimal degrees - stating and proving a number of essential theorems and outlining relevant previous work, along with some small original results. Chapter 2 calculates the minimal degrees for an infinite class of semidirect products - specifically the se

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26

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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27

PRANDELLI, MARIATERESA. "Algebra of sets, permutation groups and invariant factors." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2019. http://hdl.handle.net/10281/241257.

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Nella tesi mi occupo del problema di trovare particolari forme diagonali per le matrici di strutture di incidenza tra t-sottoinsiemi e k-sottoinsiemi (L_t,L_k; \subseteq). Denotato con X un insieme finito di n elementi e con L l’insieme delle parti di X, consideriamo i sottoinsiemi L_i di L, for i=0,…,n; dove L_i è l’insieme di tutti i sottoinsiemi di X di cardinalità i; i.e. gli elementi di L_i sono i-sottoinsiemi di X. (L_t,L_k; \subseteq) è la struttura d’incidenza così definita: per x in L_t e y in L_k, x e y sono incidenti se e solo se x è contenuto in y. La sua matrice d’incidenza è

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28

Schimanski, Nichole Louise. "Orthomorphisms of Boolean Groups." PDXScholar, 2016. http://pdxscholar.library.pdx.edu/open_access_etds/3100.

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An orthomorphism, π, of a group, (G, +), is a permutation of G with the property that the map x → -x + π(x) is also a permutation. In this paper, we consider orthomorphisms of the additive group of binary n-tuples, Zn2. We use known orthomorphism preserving functions to prove a uniformity in the cycle types of orthomorphisms that extend certain partial orthomorphisms, and prove that extensions of particular sizes of partial orthomorphisms exist. Further, in studying the action of conjugating orthomorphisms by automorphisms, we find several symmetries within the orbits and stabilizers of this a

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29

Penrod, Keith. "Infinite product groups /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1977.pdf.

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30

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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31

Lemieux, Stephane R. "Minimal degree of faithful permutation representations of finite groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0015/MQ48492.pdf.

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32

Roney-Dougal, Colva Mary. "Permutation groups with a unique nondiagonal self-paired orbital." Thesis, Queen Mary, University of London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246981.

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33

Sharp, Graham R. "Recognition algorithms for actions of permutation groups on pairs." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244602.

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34

Treacher, Helen. "The reconstruction index of semi-2-regular permutation groups." Thesis, University of East Anglia, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.429591.

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35

Blackford, J. Thomas. "Permutation groups of extended cyclic codes over Galois Rings /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488186329502909.

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36

Lemieux, Stephane R. (Stephane Robert) Carleton University Dissertation Mathematics and Statistics. "Minimal degree of faithful permutation representations of finite groups." Ottawa, 1999.

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37

Rashwan, Osama Agami. "On the composition factors of some permutation modules." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323354.

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38

Giudici, Michael Robert. "Fixed point free elements of prime order in permutation groups." Thesis, Queen Mary, University of London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252086.

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39

Inglis, Nicholas Francis John. "Multiplicity-free permutation characters, distance-transitive graphs and classical groups." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.256704.

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40

Justus, Amanda N. "Permutation Groups and Puzzle Tile Configurations of Instant Insanity II." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etd/2337.

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The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or a 5 x 4 puzzle, respectively. We consider the possibilities when we delete a color

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41

Torres, Bisquertt María de la Luz. "Symmetric generation of finite groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2625.

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Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.

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42

Xuan, Mingzhi. "On Steinhaus Sets, Orbit Trees and Universal Properties of Various Subgroups in the Permutation Group of Natural Numbers." Thesis, University of North Texas, 2012. https://digital.library.unt.edu/ark:/67531/metadc149691/.

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In the first chapter, we define Steinhaus set as a set that meets every isometric copy of another set at exactly one point. We show that there is no Steinhaus set for any four-point subset in a plane.In the second chapter, we define the orbit tree of a permutation group of natural numbers, and further introduce compressed orbit trees. We show that any rooted finite tree can be realized as a compressed orbit tree of some permutation group. In the third chapter, we investigate certain classes of closed permutation groups of natural numbers with respect to their universal and surjectively univers

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43

Pearce, Geoffrey. "Transitive decompositions of graphs." University of Western Australia. School of Mathematics and Statistics, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0087.

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A transitive decomposition of a graph is a partition of the arc set such that there exists a group of automorphisms of the graph which preserves and acts transitively on the partition. This turns out to be a very broad idea, with several striking connections with other areas of mathematics. In this thesis we first develop some general theory of transitive decompositions, and in particular we illustrate some of the more interesting connections with certain combinatorial and geometric structures. We then give complete, or nearly complete, structural characterisations of certain classes of transi

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44

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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45

Morje, Prabhav Gangadhar. "A nearly linear algorithm for Sylow subgroups of small-base permutation groups /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487932351057768.

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46

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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47

CAMPOS, JÚNIOR Walfrido Siqueira. "Permutações." Universidade Federal Rural de Pernambuco, 2014. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6711.

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Submitted by (lucia.rodrigues@ufrpe.br) on 2017-03-29T14:53:15Z No. of bitstreams: 1 Walfrido Siqueira Campos Junior.pdf: 422142 bytes, checksum: a769780b0d11bc646f87ad7036267f6b (MD5)<br>Made available in DSpace on 2017-03-29T14:53:15Z (GMT). No. of bitstreams: 1 Walfrido Siqueira Campos Junior.pdf: 422142 bytes, checksum: a769780b0d11bc646f87ad7036267f6b (MD5) Previous issue date: 2014-06-10<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>This work consists of the presentation of a simple permutation, seen as function. This function is bijective, hence admits in

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48

Kasouha, Abeir Mikhail. "Symmetric representations of elements of finite groups." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2605.

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This thesis demonstrates an alternative, concise but informative, method for representing group elements, which will prove particularly useful for the sporadic groups. It explains the theory behind symmetric presentations, and describes the algorithm for working with elements represented in this manner.

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49

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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50

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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