Linear Pro-p-Groups of Finite Width

1. Front Matter

   Pages I-VIII

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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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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.

• Lattice
• algebra
• linear-p-groups
• order with involutions over local fields
• p-acid analytic groups
• p-groups
• pro-p-groups of finite width

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