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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.

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.

Notes on Infinite Permutation Groups by Meenaxi Bhattacharjee

Title Notes on Infinite Permutation Groups
Author Meenaxi Bhattacharjee
Publisher Springer Science & Business Media
Release 1998-11-20
Category Mathematics
Total Pages 206
ISBN 9783540649656
Language English, Spanish, and French
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Book Summary:

The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions. There is basic background in both group theory and the necessary model theory, and the following topics are covered: transitivity and primitivity; symmetric groups and general linear groups; wreatch products; automorphism groups of various treelike objects; model-theoretic constructions for building structures with rich automorphism groups, the structure and classification of infinite primitive Jordan groups (surveyed); applications and open problems. With many examples and exercises, the book is intended primarily for a beginning graduate student in group theory.

Title Permutation Group Algorithms
Author Ákos Seress
Publisher Cambridge University Press
Release 2003-03-17
Category Computers
Total Pages 292
ISBN 9780521661034
Language English, Spanish, and French
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Table of contents

Ordered Permutation Groups by Andrew Martin William Glass

Title Ordered Permutation Groups
Author Andrew Martin William Glass
Publisher Cambridge University Press
Release 1981
Category Mathematics
Total Pages 266
ISBN 0521241901
Language English, Spanish, and French
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Book Summary:

As a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study, namely the set of permutations that preserves that order. In some senses. these are universal for automorphisms of models of theories. The purpose of this book is to make a thorough, comprehensive examination of these groups of permutations. After providing the initial background Professor Glass develops the general structure theory, emphasizing throughout the geometric and intuitive aspects of the subject. He includes many applications to infinite simple groups, ordered permutation groups and lattice-ordered groups. The streamlined approach will enable the beginning graduate student to reach the frontiers of the subject smoothly and quickly. Indeed much of the material included has never been available in book form before, so this account should also be useful as a reference work for professionals.

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.

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.

Title Ordered Groups and Infinite Permutation Groups
Author W.C. Holland
Publisher Springer Science & Business Media
Release 2013-12-01
Category Mathematics
Total Pages 248
ISBN 1461334438
Language English, Spanish, and French
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Book Summary:

The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that time, both P. Conrad and P. Cohn had showed that a group admits a total right ordering if and only if the group is a group of automor phisms of a totally ordered set. (In a right ordered group, the order is required to be preserved by all right translations, unlike a (two-sided) ordered group, where both right and left translations must preserve the order.

Title The Primitive Soluble Permutation Groups of Degree Less than 256
Author Mark W. Short
Publisher Springer
Release 2006-11-15
Category Mathematics
Total Pages 151
ISBN 3540471200
Language English, Spanish, and French
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Book Summary:

This monograph addresses the problem of describing all primitive soluble permutation groups of a given degree, with particular reference to those degrees less than 256. The theory is presented in detail and in a new way using modern terminology. A description is obtained for the primitive soluble permutation groups of prime-squared degree and a partial description obtained for prime-cubed degree. These descriptions are easily converted to algorithms for enumerating appropriate representatives of the groups. The descriptions for degrees 34 (die vier hochgestellt, Sonderzeichen) and 26 (die sechs hochgestellt, Sonderzeichen) are obtained partly by theory and partly by machine, using the software system Cayley. The material is appropriate for people interested in soluble groups who also have some familiarity with the basic techniques of representation theory. This work complements the substantial work already done on insoluble primitive permutation groups.

Title Notes on Infinite Permutation Groups
Author M Bhattacharjee
Publisher Springer
Release 1997-01-01
Category Mathematics
Total Pages 212
ISBN 9380250916
Language English, Spanish, and French
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Book Summary: