Point regular groups of automorphisms of generalised quadrangles

Authors:
John Bamberg;Michael Giudici
Affiliations:
Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, 6009 W.A., Australia;Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, 6009 W.A., Australia
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

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Abstract

We study the point regular groups of automorphisms of some of the known generalised quadrangles. In particular we determine all point regular groups of automorphisms of the thick classical generalised quadrangles. We also construct point regular groups of automorphisms of the generalised quadrangle of order (q-1,q+1) obtained by Payne derivation from the classical symplectic quadrangle W(3,q). For q=p^f with f=2 we obtain at least two nonisomorphic groups when p=5 and at least three nonisomorphic groups when p=2 or 3. Our groups include nonabelian 2-groups, groups of exponent 9 and nonspecial p-groups. We also enumerate all point regular groups of automorphisms of some small generalised quadrangles.