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Other titles in the Lecture Notes in Computer Science series:

Lecture Notes in Computer Science #1674: Linear Pro-P-Groups of Finite Width

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Lecture Notes in Computer Science #1674: Linear Pro-P-Groups of Finite Width Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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

Introduction.- Elementary properties of width.- p-adically simple groups (ß-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.- References.- Notation.- Index.

Product Details

ISBN:
9783540636434
Author:
Klaas, G.
Publisher:
Springer
Author:
Leedham-Green, C. R.
Author:
Klaas, Gundel
Author:
Klass, G.
Author:
Leedham-Green, Charles R.
Author:
Plesken, Wilhelm
Location:
Berlin, Heidelberg
Subject:
Algebra - Linear
Subject:
Linear algebraic groups
Subject:
p-adic groups.
Subject:
Profinite groups.
Subject:
Group Theory
Subject:
Algebra - Abstract
Subject:
linear-p-groups
Subject:
order with involutions over local fields
Subject:
p-acid analytic groups
Subject:
p-groups
Subject:
pro-p-groups of finite width
Subject:
Group Theory and Generalizations
Subject:
Mathematics-Linear Algebra
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Description:
Book
Series:
Lecture Notes in Mathematics
Series Volume:
1674
Publication Date:
19971118
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
123
Dimensions:
235 x 155 mm 410 gr

Related Subjects

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Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Group Theory

Lecture Notes in Computer Science #1674: Linear Pro-P-Groups of Finite Width New Trade Paper
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Product details 123 pages Springer - English 9783540636434 Reviews:
"Synopsis" by , 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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