Finite Primitive Permutation Groups: a Survey PDF Download
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Author: C. E. Praeger
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Author: C. E. Praeger
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Author: Nick Gill
Publisher: Springer Nature
ISBN: 3030959562
Category : Mathematics
Languages : en
Pages : 221
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Book Description
This book gives a proof of Cherlin’s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan’s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. The first part gives a full introduction to Cherlin’s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest to a wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.
Author: Helmut Wielandt
Publisher: Academic Press
ISBN: 1483258297
Category : Mathematics
Languages : en
Pages : 125
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Book Description
Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.
Author: Peter J. Cameron
Publisher: Cambridge University Press
ISBN: 9780521653787
Category : Mathematics
Languages : en
Pages : 236
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Book Description
This book summarizes recent developments in the study of permutation groups for beginning graduate students.
Author: John D. Dixon
Publisher: Springer Science & Business Media
ISBN: 1461207312
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. With its many exercises and detailed references to the current literature, this text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, as well as for self-study.
Author: L.G. Kovacs
Publisher: Springer
ISBN: 3540469001
Category : Mathematics
Languages : en
Pages : 209
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Book Description
Author: C. E. Praeger
Publisher:
ISBN:
Category :
Languages : en
Pages : 9
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Author: Rosemary Bailey
Publisher: Cambridge University Press
ISBN: 0521598400
Category : Analyse combinatoire
Languages : en
Pages : 356
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Book Description
The invited lectures given at the 16th. British Combinatorial Conference, July 1997 at Queen Mary and Westfield College.
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
ISBN: 082184654X
Category : Mathematics
Languages : en
Pages : 87
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Book Description
Addresses the classical problem of determining finite primitive permutation groups G with a regular subgroup B.
Author: Hua Zhang
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659176692
Category : Finite simple groups
Languages : en
Pages : 184
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Book Description
In the past 60 years interactions between group theory and the theory of graphs have greatly stimulated the development of each other, especially the theory of symmetric graphs (or more generally vertex-transitive graphs) has almost developed in parallel with the theory of permutation groups. The aim of this thesis is to make an e ort, both in terms of pure research and broader value, to solve some challenging problems in these two elds. First we considered the problem of classifying nite primitive permutation groups with soluble stabilizers. This problem has a very long history. By the O'Nan-Scott Theorem, such groups are of type a ne, almost simple, and product action. We reduced the product action type to the almost simple type, and for the latter, a complete classi cation was given, which forms the main result of the thesis. The main result was then used to solve some problems in algebraic graph theory. The rst application of which is to classify edge-primitive s-arc-transitive graphs for s 4. After undertaking a general study on the local structures of 2-path-transitive graphs, we presented the second application by classifying nite vertex-primitive and vertex-biprimitive 2-path-transitive graphs. The result then helps us to be able to construct some new half-transitive graphs. Another application of the main result is that a complete classi cation of nite vertexbiprimitive edge-transitive tetravalent graphs is given (recall that for the cubic case, the classi cation was given by Ivanov and Io nova in a highly cited article in 1985).
