Regular Sets and Geometric Groups |
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Authors: | Jennifer D Key Johannes Siemons |
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Institution: | 1. Department of Mathematics, University of Birmingham, PO Box 363, Birmingham, B15 2TT, UK 2. School of Mathematics and Physics, University of East Anglia, University Plain, Norwich, NR4 7TJ, UK
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Abstract: | If G is a permutation group acting on a set Ω, a subset Λ of Ω is called a regular set for G if the set-stabilizer of Λ in G is the identity subgroup. We show here that the projective and affine semi-linear groups acting in the natural way as permutation groups on their respective finite geometries, have, in general, for all finite dimensions and all finite fields, regular sets of points. The exceptions to this are found, and an extension of the results to infinite fields is discussed. |
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