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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