Basic coset geometries

Details Basic coset geometries Basic coset geometries

2010-10-04

arxiv.org/abs/1010.0481v2

Mathematics

Group Theory

Changes made following referees' comments. This includes determining the diagrams of some of the constructions

Scientific paper

In earlier work we gave a characterisation of pregeometries which are `basic' (that is, admit no `non-degenerate' quotients) relative to two different kinds of quotient operations, namely imprimitive quotients and normal quotients. Each basic geometry was shown to involve a faithful group action, which is primitive or quasiprimitive respectively, on the set of elements of each type. For each O'Nan-Scott type of primitive group, we construct a new infinite family of geometries, which are thick and of unbounded rank, and which admit a flag-transitive automorphism group acting faithfully on the set of elements of each type as a primitive group of the given O'Nan-Scott type.

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