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The existence of Fano subplanes in generalized Hall planes

Published online by Cambridge University Press:  09 April 2009

A. J. Rahilly
A. J. Rahilly
Affiliation:
University of SydneySydney, New South Wales, Australia
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One of the best known classes of non-Desarguesian planes is the calss of Hall planes (see Hall [2]). In [6] Hanna Neumann showed that the finite Hall planes of old order possess subplanes of order two (i.e., Fano subplanes)1. Kirkpatrick [5] has considered a type of plane which is generalization of the Hall planes and which he calls generalized Hall planes. In this paper we will give a sufficient condition that a finite generalized Hall plane possesses Fano subplanes. Some examples of odd order planes to which the condition applies shall be exhibited.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 2 , September 1973 , pp. 234 - 238
Copyright
Copyright © Australian Mathematical Society 1973

References

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