Generalized quadrangles admitting a sharply transitive Heisenberg group |
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Authors: | S De Winter K Thas |
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Institution: | (1) Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, 9000 Ghent, Belgium |
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Abstract: | All known finite generalized quadrangles that admit an automorphism group acting sharply transitively on their point set arise
by Payne derivation from thick elation generalized quadrangles of order s with a regular point. In these examples only two groups occur: elementary abelian groups of even order and odd order Heisenberg
groups of dimension 3. In 2] the authors determined all generalized quadrangles admitting an abelian group with a sharply
transitive point action. Here, we classify thick finite generalized quadrangles admitting an odd order Heisenberg group of
dimension 3 acting sharply transitively on the points. In fact our more general result comes close to a complete solution
of classifying odd order Singer p-groups.
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Keywords: | Generalized quadrangle Singer group Heisenberg group Payne derivation |
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