Linear Pro-p-Groups of Finite Width / Edition 1

Linear Pro-p-Groups of Finite Width / Edition 1

by Gundel Klaas, Wilhelm Plesken, Charles R. Leedham-Green
     
 

ISBN-10: 3540636439

ISBN-13: 9783540636434

Pub. Date: 11/18/1997

Publisher: Springer Berlin Heidelberg

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

Overview

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.

Product Details

ISBN-13:
9783540636434
Publisher:
Springer Berlin Heidelberg
Publication date:
11/18/1997
Series:
Lecture Notes in Mathematics Series, #1674
Edition description:
1997
Pages:
123
Product dimensions:
9.21(w) x 6.14(h) x 0.26(d)

Table of Contents

Elementary properties of width.- p-adically simple groups .- Periodicity.- Chevalley groups.- Some classical groups.- Some thin groups.- Algorithms on fields.- Fields of small degree.- Algorithm for finding a filtration and the obliquity.- The theory behind the tables.- Tables.- Uncountably many just infinite pro-p-groups of finite width.- Some open problems.

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