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

  • Book
  • © 1987

Overview

Authors:
  1. Herbert Abels
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1261)

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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

Table of contents (8 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction

    • Herbert Abels
    Pages 1-14

  3. Compact presentability and contracting automorphisms

    • Herbert Abels
    Pages 15-26

  4. Filtrations of Lie algebras and groups

    • Herbert Abels
    Pages 27-48

  5. A necessary condition for compact presentability

    • Herbert Abels
    Pages 49-60

  6. Implications of the necessary condition

    • Herbert Abels
    Pages 61-89

  7. The second homology

    • Herbert Abels
    Pages 90-122

  8. S-arithmetic groups

    • Herbert Abels
    Pages 123-145

  9. S-arithmetic solvable groups

    • Herbert Abels
    Pages 146-168

  10. Back Matter

    Pages 169-178
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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, Lie Groups

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