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Line-rank 3 affine planes

Published online by Cambridge University Press:  17 April 2009

Michael J. Kallaher  and
Graham Kelly
Michael J. Kallaher
Affiliation:
Department of Mathematics, Washington State University, Pullman, Washington 98164, USA
Graham Kelly
Affiliation:
AMP Society, GPO Box 4134, Sydney, New South Wales 2001, Australia.
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Abstract

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We consider finite affine planes having a collineation group acting as a rank 3 permutation group on the affine lines. By a classical result of A. Wagner, such affine planes are translation planes. We show that if, in addition, the plane has odd dimension or dimension 2 over its kernel, then the plane is Desarguesian.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 3 , June 1982 , pp. 397 - 403
Copyright
Copyright © Australian Mathematical Society 1982

References

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