Basic coset geometries

Authors:
Michael Giudici;Geoffrey Pearce;Cheryl E. Praeger
Affiliations:
Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, University of Western Australia, Crawley, Australia 6009;Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, University of Western Australia, Crawley, Australia 6009;Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, University of Western Australia, Crawley, Australia 6009
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2012

Citing 4
Cited 1

Classifying geometries with CAYLEY

Journal of Symbolic Computation
The MAGMA algebra system I: the user language

Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Basic and degenerate pregeometries

European Journal of Combinatorics
Quotients of incidence geometries

Designs, Codes and Cryptography

Basic and degenerate pregeometries

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

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 operation, namely taking 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.