Infinite Linear Groups

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Infinite Linear Groups

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Author : Bertram Wehrfritz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Infinite Linear Groups written by Bertram Wehrfritz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.

Infinite Linear Groups

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Author : Bertram Wehrfritz
language : en
Publisher:
Release Date : 2014-01-15

Infinite Linear Groups written by Bertram Wehrfritz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Algebra Iv

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Author : A.I. Kostrikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algebra Iv written by A.I. Kostrikin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Group theory is one of the most fundamental branches of mathematics. This volume of the Encyclopaedia is devoted to two important subjects within group theory. The first part of the book is concerned with infinite groups. The authors deal with combinatorial group theory, free constructions through group actions on trees, algorithmic problems, periodic groups and the Burnside problem, and the structure theory for Abelian, soluble and nilpotent groups. They have included the very latest developments; however, the material is accessible to readers familiar with the basic concepts of algebra. The second part treats the theory of linear groups. It is a genuinely encyclopaedic survey written for non-specialists. The topics covered includethe classical groups, algebraic groups, topological methods, conjugacy theorems, and finite linear groups. This book will be very useful to allmathematicians, physicists and other scientists including graduate students who use group theory in their work.

Infinite Linear Groups

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Author : B. A. F. Wehrfritz
language : en
Publisher:
Release Date : 1972

Infinite Linear Groups written by B. A. F. Wehrfritz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Infinite groups categories.

Notes On Infinite Permutation Groups

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Author : Meenaxi Bhattacharjee
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-11-20

Notes On Infinite Permutation Groups written by Meenaxi Bhattacharjee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-20 with Mathematics categories.

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.

Infinite Group Theory From The Past To The Future

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Author : Paul Baginski
language : en
Publisher: World Scientific
Release Date : 2017-12-26

Infinite Group Theory From The Past To The Future written by Paul Baginski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-26 with Mathematics categories.

The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest.

Infinite Linear Groups

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Author : Bertram A. F. Wehrfritz
language : de
Publisher:
Release Date : 1973

Infinite Linear Groups written by Bertram A. F. Wehrfritz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.

Linear Groups

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Author : Martyn R. Dixon
language : en
Publisher: CRC Press
Release Date : 2020-04-03

Linear Groups written by Martyn R. Dixon and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Mathematics categories.

Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. The array of articles devoted to this topic is enormous, and there are many monographs concerned with matrix groups, ranging from old, classical texts to ones published more recently. However, in the case when the dimension is infinite (and such cases arise quite often), the reality is quite different. The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups, in the transition from the study of finite groups to the study of infinite groups which appeared about one hundred years ago. It is well known that this transition was extremely efficient and led to the development of a rich and central branch of algebra: Infinite group theory. The hope is that this book can be part of a similar transition in the field of linear groups. Features This is the first book dedicated to infinite-dimensional linear groups This is written for experts and graduate students specializing in algebra and parallel disciplines This book discusses a very new theory and accumulates many important and useful results

Notes On Infinite Permutation Groups

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Author : Meenaxi Bhattacharjee
language : en
Publisher: Springer
Release Date : 2006-11-14

Notes On Infinite Permutation Groups written by Meenaxi Bhattacharjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

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.

Matrix Groups

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Author : Dmitriĭ Alekseevich Suprunenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1976

Matrix Groups written by Dmitriĭ Alekseevich Suprunenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.

This volume is a translation from the Russian of D.A. Suprunenko's book which was published in the Soviet Union in 1972. The translation was edited by K.A. Hirsch. The book gives an account of the classical results on the structure of normal subgroups of the general linear group over a division ring, of Burnside's and Schur's theorems on periodic linear groups, and of the theorem on the normal structure of SL(n, Z) for n >2. The theory of solvable, nilpotent, and locally nilpotent linear groups is also discussed.