Skew linear groups

Skew linear groups

by Shirvani, M.

Type Book
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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…

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Title Statements

  • Full title :Skew linear groups / M. Shirvani and B.A.F. Wehrfritz.

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.

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Edition Statements

  • Publication Date:©1986.

Publication Statements

Notes

Includes indexes.

The Physical Object

  • Description:1 online resource (253 pages)

Edition Identifiers

  • ISBN:9781107361379, 1107361370, 9780511600630, 0511600631, 1139881779, 9781139881777, 1107366283, 9781107366282, 1107371007, 9781107371002, 1107368626, 9781107368620, 1299404073, 9781299404076, 1107363829, 9781107363823
  • oclc:ocn839547826
  • LC Classification:QA171
  • Dewey Decimal:512/.2

Table of 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 Di…

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Subjects

Corps gauches Division rings Endliche Gruppe Finite groups Groupes de matrices Groupes finis MATHEMATICS -- Group Theory Matrices, Groupes de Matrix groups Schiefgruppenring Skew fields

Writers

Shirvani, M. Wehrfritz, Bertram A. F.

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