Skew linear groups / M. Shirvani and B.A.F. Wehrfritz.

Format:

Book

Author/Creator:

Shirvani, M., author.

Wehrfritz, Bertram A. F., author.

Series:

London Mathematical Society lecture note series ; 118.

London Mathematical Society lecture note series ; 118

Language:

English

Subjects (All):

Finite groups.

Division rings.

Matrix groups.

Physical Description:

1 online resource (253 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1986.

Language Note:

English

Summary:

This book is concerned with subgroups of groups of the form GL(n,D) for some division ring D. In it the authors bring together many of the advances in the theory of skew linear groups. Some aspects of skew linear groups are similar to those for linear groups, however there are often significant differences either in the method of proof or the results themselves. Topics covered in this volume include irreducibility, unipotence, locally finite-dimensional division algebras, and division algebras associated with polycyclic groups. Both authors are experts in this area of current interest in group theory, and algebraists and research students will find this an accessible account of the subject.

Contents:

Cover; Title; Copyright; Contents; 1. BASIC CONCEPTS; 1.1 Irreducibility; 1.2 Absolute Irreducibility; 1.3 Unipotence; 1.4 Constructions; 2. FINITE AND LOCALLY FINITE GROUPS; 2.1 Finite Subgroups of Division Rings; 2.2 The Schur Index; 2.3 Locally Finite Skew Linear Groups of Positive Characteristic; 2.4 The Theorems of Zalesskii and Hartley & Shahabi; 2.5 Locally Finite Skew Linear Groups of Characteristic Zero; 3. LOCALLY FINITE-DIMENSIONAL DIVISION ALGEBRAS; 3.1 General Techniques; 3.2 Locally Nilpotent Groups; 3.3 Locally Soluble Groups; 3.4 The Upper Central Series

3.5 Engel Elements and Generalized Nilpotent Groups4. DIVISION RINGS ASSOCIATED WITH POLYCYCLIC GROUPS; 4.1 Generalities and Examples; 4.2 Residual Finiteness; 4.3 Residual Nilpotence; 4.4 Division Rings of Quotients of Group Algebras; 4.5 Free Subgroups of Normal Subgroups of General Linear Groups; 4.6 Universal Enveloping Algebras of Lie Algebras; 5. NORMAL SUBGROUPS OF ABSOLUTELY IRREDUCIBLE GROUPS; 5.1 Normal Subgroups of Linear Groups; 5.2 Automorphisms of Certain Semisimple Algebras; 5.3 Recognizing Crossed Products; 5.4 Locally Finite Normal Subgroups of Skew Linear Groups

5.5 Locally Finite-Dimensional Division Algebras5.6 Soluble Normal Subgroups of Skew Linear Groups; 5.7 Generalized Soluble Groups; 6 AN APPLICATION TO GROUP RINGS; 6.1 Preliminaries; 6.2 Soluble Groups; 6.3 Locally Finite Groups; BIBLIOGRAPHY; NOTATION INDEX; AUTHOR INDEX; GENERAL INDEX

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and indexes.

ISBN:

1-139-88177-9

1-107-36628-3

1-107-37100-7

1-107-36137-0

1-107-36862-6

1-299-40407-3

1-107-36382-9

0-511-60063-1