Infinite Linear Groups: An Account of the Group-theoretic Properties of Infinite Groups of Matrices

Wehrfritz, B.A.F.

ISBN 10: 3540061320 / ISBN 13: 9783540061328

Published by Springer-verlag, New York, 1973

About this Item

An ex-library copy in yellow cloth lettered in black, with the usual ex-libris markings. The binding is sound, the text is clean/unmarked, and there is little cover wear. No dust jacket.

Seller Inventory # 056293

Bibliographic Details

• Title: Infinite Linear Groups: An Account of the Group-theoretic Properties of Infinite Groups of Matrices
• Publisher: Springer-verlag, New York
• Publication Date: 1973
• Language: English
• ISBN 10: 3540061320
• ISBN 13: 9783540061328
• Binding: Hardcover
• Edition: First U.S. Edition.
• Condition: Good
• Dust Jacket Condition: No Dust Jacket
• Book Type: Book

About this title

Synopsis

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.