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Collineation groups which are sharply transitive on an oval

Published online by Cambridge University Press:  17 April 2009

P.B. Kirkpatrick
P.B. Kirkpatrick
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
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Abstract

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Let G be a group of collineations in a protective plane Π of order n. Suppose that one of the point orbits of G is an oval of Π, and that G acts regularly on this orbit. We prove that G fixes a non-incident point-line pair if either n is even, or n is odd and G is abelian, or n ≠ 11, 23, 59 is odd and is a pseudo-conic. It is then easy to deduce information about the lengths of the other orbits of G, and about the structure of G as an abstract group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 2 , October 1974 , pp. 197 - 211
Copyright
Copyright © Australian Mathematical Society 1974

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