Basic coset geometries
Abstract
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.
Cite
@article{arxiv.1010.0481,
title = {Basic coset geometries},
author = {Michael Giudici and Geoffrey Pearce and Cheryl E. Praeger},
journal= {arXiv preprint arXiv:1010.0481},
year = {2011}
}
Comments
Changes made following referees' comments. This includes determining the diagrams of some of the constructions