Linear Pro-p-Groups of Finite Width

Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken (auth.)3540636439, 9783540636434

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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Table of contents :
Introduction….Pages 1-8
Elementary properties of width….Pages 9-11
p -adically simple groups $$(tilde p – groups)$$ ….Pages 12-20
Periodicity….Pages 21-25
Chevalley groups….Pages 26-29
Some classical groups….Pages 30-54
Some thin groups….Pages 55-58
Algorithms on fields….Pages 59-61
Fields of small degree….Pages 62-67
Algorithm for finding a filtration and the obliquity….Pages 68-77
The theory behind the tables….Pages 78-91
Tables….Pages 92-105
Uncountably many just infinite pro- p -groups of finite width….Pages 106-107
Some open problems….Pages 108-108