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Linear Pro-p-Groups of Finite Width

  • Book
  • © 1997

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Authors:
  1. Gundel Klaas
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  2. Charles R. Leedham-Green
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  3. Wilhelm Plesken
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1674)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-VIII
    Download chapter PDF

  2. Introduction

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 1-8

  3. Elementary properties of width

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 9-11

  4. p-adically simple groups \((\tilde p - groups)\)

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 12-20

  5. Periodicity

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 21-25

  6. Chevalley groups

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 26-29

  7. Some classical groups

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 30-54

  8. Some thin groups

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 55-58

  9. Algorithms on fields

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 59-61

  10. Fields of small degree

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 62-67

  11. Algorithm for finding a filtration and the obliquity

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 68-77

  12. The theory behind the tables

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 78-91

  13. Tables

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 92-105

  14. Uncountably many just infinite pro-p-groups of finite width

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 106-107

  15. Some open problems

    • Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken
    Pages 108-108

  16. Back Matter

    Pages 109-115
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Keywords

About this book

The normal subgroup structure of maximal pro-p-subgroups of rational points of algebraic groups over the p-adics and their characteristic p analogues are investigated. These groups have finite width, i.e. the indices of the sucessive terms of the lower central series are bounded since they become periodic. The richness of the lattice of normal subgroups is studied by the notion of obliquity. All just infinite maximal groups with Lie algebras up to dimension 14 and most Chevalley groups and classical groups in characteristic 0 and p are covered. The methods use computers in small cases and are purely theoretical for the infinite series using root systems or orders with involutions.

Bibliographic Information

  • Book Title: Linear Pro-p-Groups of Finite Width

  • Authors: Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0094086

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-63643-4Published: 04 November 1997

  • eBook ISBN: 978-3-540-69623-0Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 116

  • Topics: Group Theory and Generalizations

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