Basic coset geometries
Michael Giudici
, Geoffrey Pearce
and Cheryl E. Praeger
Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, University of Western Australia, Crawley, WA, 6009, Australia
DOI: 10.1007/s10801-012-0350-8
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.
Pages: 561–594
Keywords: incidence geometries; primitive permutation group
Full Text: PDF
References
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