Linear Pro-P-Groups of Finite Width

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 pe...

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Bibliographic Details
Main Authors Klaas, Gundel, Leedham-Green, Charles R, Plesken, Wilhelm
Format eBook
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin / Heidelberg 2006
Springer Berlin Heidelberg
Springer
Edition1
SeriesLecture Notes in Mathematics
Subjects
Finite groups
Group theory
Group Theory and Generalizations
Linear algebraic groups
Mathematics
Mathematics and Statistics
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Summary: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.
ISBN:9783540636434
3540636439
9783662165942
3662165945
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0094086