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Finite Permutation Groups by Helmut Wielandt

Title Finite Permutation Groups
Author Helmut Wielandt
Publisher Academic Press
Release 2014-05-10
Category Mathematics
Total Pages 124
ISBN 1483258297
Language English, Spanish, and French
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Book Summary:

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.

Permutation Groups by John D. Dixon

Title Permutation Groups
Author John D. Dixon
Publisher Springer Science & Business Media
Release 2012-12-06
Category Mathematics
Total Pages 348
ISBN 1461207312
Language English, Spanish, and French
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Book Summary:

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.

Title Cherlin s Conjecture for Finite Primitive Binary Permutation Groups
Author Nick Gill
Publisher Springer Nature
Release 2022-07-18
Category Mathematics
Total Pages 216
ISBN 3030959562
Language English, Spanish, and French
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Book Summary:

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.

Finite permutation groups tr by Helmut Wielandt

Title Finite permutation groups tr
Author Helmut Wielandt
Publisher
Release
Category Group theory
Total Pages
ISBN
Language English, Spanish, and French
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Permutation Groups by Peter J. Cameron

Title Permutation Groups
Author Peter J. Cameron
Publisher Cambridge University Press
Release 1999-02-04
Category Mathematics
Total Pages 220
ISBN 9780521653787
Language English, Spanish, and French
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Book Summary:

This book summarizes recent developments in the study of permutation groups for beginning graduate students.

Finite Permutation Groups by Cheryl E. Praeger

Title Finite Permutation Groups
Author Cheryl E. Praeger
Publisher
Release 1973
Category Group theory
Total Pages 113
ISBN 9780521360630
Language English, Spanish, and French
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Oligomorphic Permutation Groups by Peter J. Cameron

Title Oligomorphic Permutation Groups
Author Peter J. Cameron
Publisher Cambridge University Press
Release 1990-06-29
Category Mathematics
Total Pages 160
ISBN 0521388368
Language English, Spanish, and French
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Book Summary:

The study of permutations groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. This book discusses such structures, their substructures and their automorphism groups using a wide range of techniques.

Title Permutation Groups and Cartesian Decompositions
Author Cheryl E. Praeger
Publisher Cambridge University Press
Release 2018-05-03
Category Mathematics
Total Pages
ISBN 131699905X
Language English, Spanish, and French
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Book Summary:

Permutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nan–Scott theory are presented not only for primitive permutation groups but also for the larger families of quasiprimitive and innately transitive groups, including several classes of infinite permutation groups. Their precision is sharpened by the introduction of a cartesian decomposition concept. This facilitates reduction arguments for primitive groups analogous to those, using orbits and partitions, that reduce problems about general permutation groups to primitive groups. The results are particularly powerful for finite groups, where the finite simple group classification is invoked. Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures. Students and researchers with an interest in mathematical symmetry will find the book enjoyable and useful.

On Finite Permutation Groups by Christian Ronse

Title On Finite Permutation Groups
Author Christian Ronse
Publisher
Release 1979
Category Group theory
Total Pages 246
ISBN
Language English, Spanish, and French
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Book Summary: