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  • © 1987

Finite Presentability of S-Arithmetic Groups. Compact Presentability of Solvable Groups

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1261)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VI
  2. Introduction

    • Herbert Abels
    Pages 1-14
  3. Filtrations of Lie algebras and groups

    • Herbert Abels
    Pages 27-48
  4. Implications of the necessary condition

    • Herbert Abels
    Pages 61-89
  5. The second homology

    • Herbert Abels
    Pages 90-122
  6. S-arithmetic groups

    • Herbert Abels
    Pages 123-145
  7. S-arithmetic solvable groups

    • Herbert Abels
    Pages 146-168
  8. Back Matter

    Pages 169-178

About this book

The problem of determining which S-arithmetic groups have a finite presentation is solved for arbitrary linear algebraic groups over finite extension fields of #3. For certain solvable topological groups this problem may be reduced to an analogous problem, that of compact presentability. Most of this monograph deals with this question. The necessary background material and the general framework in which the problem arises are given partly in a detailed account, partly in survey form. In the last two chapters the application to S-arithmetic groups is given: here the reader is assumed to have some background in algebraic and arithmetic group. The book will be of interest to readers working on infinite groups, topological groups, and algebraic and arithmetic groups.

Keywords

  • algebra
  • algebraic group
  • automorphism
  • finite group
  • homology
  • lie algebra
  • linear algebra
  • topological group

Bibliographic Information

  • Book Title: Finite Presentability of S-Arithmetic Groups. Compact Presentability of Solvable Groups

  • Authors: Herbert Abels

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0079708

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-17975-7Published: 10 July 1987

  • eBook ISBN: 978-3-540-47198-1Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 182

  • Topics: Group Theory and Generalizations, Topological Groups and Lie Groups

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions