Notes on Infinite Permutation Groups

Notes on Infinite Permutation Groups

Author: Meenaxi Bhattacharjee

Publisher: Springer Science & Business Media

Published: 1998-11-20

Total Pages: 224

ISBN-13: 9783540649656

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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.


Notes on Infinite Permutation Groups

Notes on Infinite Permutation Groups

Author: Meenaxi Bhattacharjee

Publisher: Springer

Published: 2006-11-14

Total Pages: 206

ISBN-13: 3540498133

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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.


Permutation Groups

Permutation Groups

Author: John D. Dixon

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 360

ISBN-13: 1461207312

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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.


Ordered Groups and Infinite Permutation Groups

Ordered Groups and Infinite Permutation Groups

Author: W.C. Holland

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 252

ISBN-13: 1461334438

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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.


Representations of the Infinite Symmetric Group

Representations of the Infinite Symmetric Group

Author: Alexei Borodin

Publisher: Cambridge University Press

Published: 2017

Total Pages: 169

ISBN-13: 1107175550

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An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.


Permutation Groups and Cartesian Decompositions

Permutation Groups and Cartesian Decompositions

Author: Cheryl E. Praeger

Publisher: London Mathematical Society Le

Published: 2018-05-03

Total Pages: 338

ISBN-13: 0521675065

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Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.


Oligomorphic Permutation Groups

Oligomorphic Permutation Groups

Author: Peter J. Cameron

Publisher: Cambridge University Press

Published: 1990-06-29

Total Pages: 172

ISBN-13: 0521388368

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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.


Tits Buildings and the Model Theory of Groups

Tits Buildings and the Model Theory of Groups

Author: Katrin Tent

Publisher: Cambridge University Press

Published: 2002-01-03

Total Pages: 314

ISBN-13: 9780521010634

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Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.


Combinatorics of Coxeter Groups

Combinatorics of Coxeter Groups

Author: Anders Bjorner

Publisher: Springer Science & Business Media

Published: 2006-02-25

Total Pages: 371

ISBN-13: 3540275967

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Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups