Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T22:08:16.745Z Has data issue: false hasContentIssue false

A note on generalized Hall planes

Published online by Cambridge University Press:  17 April 2009

N.L. Johnson
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove that if π is a generalized Hall plane of odd order with associated Baer subplane π0 then π is a Hall plane if and only if there is a collineation σ of π such that π0σ ∩ π0 is an affine point.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Albert, A.A., “The finite planes of Ostrom”, Bol. Soc. Mat. Mexicana 11 (1966), 113.Google Scholar
[2]Johnson, N.L., “A characterization of generalized Hall planes”, Bull. Austral. Math. Soc. 6 (1972), 6167.CrossRefGoogle Scholar
[3]Johnson, N.L., “Collineation groups of derived semifield planes”, (to appear).Google Scholar
[4]Kirkpatrick, P.B., “Generalization of Hall planes of odd order”, Bull. Austral. Math. Soc. 4 (1971), 205209.CrossRefGoogle Scholar
[5]Kirkpatrick, P.B., “A characterization of the Hall planes of odd order”, Bull. Austral. Math. Soc. 6 (1972), 407415.CrossRefGoogle Scholar
[6]Ostrom, T.G., “Vector spaces and construction of finite projective planes”, Arch. Math. 19 (1968), 125.CrossRefGoogle Scholar