© 1993

Algebra IV

Infinite Groups. Linear Groups

  • A. I. Kostrikin
  • I. R. Shafarevich

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 37)

Table of contents

  1. Front Matter
    Pages i-vii
  2. A. Yu. Ol’shanskij, A. L. Shmel’kin
    Pages 1-95
  3. A. E. Zalesskij
    Pages 97-196
  4. Back Matter
    Pages 197-206

About this book


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.


Allgemeine lineare Gruppe Auflösbare Gruppen Endlich darstellbare Gruppen Finitely Presented Groups Free Groups Freie Gruppen Group theory Kombinatorische Gruppentheorie Nilpotent Groups Nilpotente Gruppen algebra algorithm linear optimization

Editors and affiliations

  • A. I. Kostrikin
    • 1
  • I. R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

Bibliographic information

  • Book Title Algebra IV
  • Book Subtitle Infinite Groups. Linear Groups
  • Editors A.I. Kostrikin
    I.R. Shafarevich
  • Series Title Encyclopaedia of Mathematical Sciences
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-53372-6
  • Softcover ISBN 978-3-642-08100-2
  • eBook ISBN 978-3-662-02869-8
  • Series ISSN 0938-0396
  • Edition Number 1
  • Number of Pages X, 206
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Original Russian edition published by VINITI, Moscow, 1989
  • Topics Group Theory and Generalizations
    Topological Groups, Lie Groups
  • Buy this book on publisher's site