Linear pro-p-groups of finite width
Author(s)
Bibliographic Information
Linear pro-p-groups of finite width
（Lecture notes in mathematics, 1674）
Springer, c1997
Available at 90 libraries
Note
Includes bibliographical references and index
Description and Table of Contents
Description
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.
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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