Linear Pro-p-Groups of Finite Width
Klaas, Gundel.
Linear Pro-p-Groups of Finite Width [electronic resource] / by Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken. - VIII, 116 p. online resource. - Lecture Notes in Mathematics, 1674 0075-8434 ; . - Lecture Notes in Mathematics, 1674 .
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.
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.
9783540696230
10.1007/BFb0094086 doi
Group theory.
Group Theory and Generalizations.
QA174-183
512.2
Linear Pro-p-Groups of Finite Width [electronic resource] / by Gundel Klaas, Charles R. Leedham-Green, Wilhelm Plesken. - VIII, 116 p. online resource. - Lecture Notes in Mathematics, 1674 0075-8434 ; . - Lecture Notes in Mathematics, 1674 .
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.
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.
9783540696230
10.1007/BFb0094086 doi
Group theory.
Group Theory and Generalizations.
QA174-183
512.2