Basic coset geometries |
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Authors: | Michael Giudici Geoffrey Pearce Cheryl E Praeger |
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Institution: | 1. Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, University of Western Australia, Crawley, WA, 6009, Australia
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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. |
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