Linear Pro-p-Groups of Finite Width

1997
ISBN: 978-3-540-63643-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1674, 116 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 201 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Klaas, Gundel

Plesken, Wilhelm

Leedham-Green, Charles R.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

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.