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Lecture Notes in Mathematics

By: G. Klaas, G. Klass, C. R. Leedham-Green

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Paperback | 4 November 1997

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124 Pages

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24.13 x 16.51 x 0.64

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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.

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Non-Fiction Mathematics Groups & Group Theory Algebra

Introduction	p. 1
Elementary properties of width	p. 9
p-adically simple groups (p-groups)	p. 12
Periodicity	p. 21
Chevalley groups	p. 26
Some classical groups	p. 30
Some thin groups	p. 55
Algorithms on fields	p. 59
Fields of small degree	p. 62
Algorithm for finding a filtration and the obliquity	p. 68
The theory behind the tables	p. 78
Tables	p. 92
Uncountably many just infinite pro-p-groups of finite width	p. 106
Some open problems	p. 108
References	p. 109
Notation	p. 113
Index	p. 115
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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