Notes on Infinite Permutation Groups

Notes on Infinite Permutation Groups
Author: Meenaxi Bhattacharjee
Publisher: Springer
Total Pages: 206
Release: 2006-11-14
Genre: Mathematics
ISBN: 3540498133

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 Science & Business Media
Total Pages: 224
Release: 1998-11-20
Genre: Mathematics
ISBN: 9783540649656

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
Total Pages: 360
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461207312

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
Total Pages: 252
Release: 2013-12-01
Genre: Mathematics
ISBN: 1461334438

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
Total Pages: 169
Release: 2017
Genre: Mathematics
ISBN: 1107175550

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
Total Pages: 338
Release: 2018-05-03
Genre: Mathematics
ISBN: 0521675065

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
Total Pages: 172
Release: 1990-06-29
Genre: Mathematics
ISBN: 0521388368

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.

Combinatorics of Coxeter Groups

Combinatorics of Coxeter Groups
Author: Anders Bjorner
Publisher: Springer Science & Business Media
Total Pages: 371
Release: 2006-02-25
Genre: Mathematics
ISBN: 3540275967

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

Tits Buildings and the Model Theory of Groups

Tits Buildings and the Model Theory of Groups
Author: Katrin Tent
Publisher: Cambridge University Press
Total Pages: 314
Release: 2002-01-03
Genre: Mathematics
ISBN: 9780521010634

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