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Characterizations of the Generalized Hughes Planes

Published online by Cambridge University Press:  20 November 2018

Heinz Lüneburg
Heinz Lüneburg*
Affiliation:
Universität Kaiserslautern, Kaiser slautern, Bundesrepublik Deutschland
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Let be a projective plane and a subplane of . If l is a line of , we let denote the group of all elations in that have as axis and leave Q invariant. In [12, p. 921], Ostrom asked for a description of all finite planes that have a Baer subplane with the property that for all lines l of . Here denotes the order of G. Both the desarguesian planes of square order and the generalized Hughes planes have this property (Hughes [10], Ostrom [14], Dembowski [6]). One of the aims of this paper is to show that these are the only planes having such a Baer subplane.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 376 - 402
Copyright
Copyright © Canadian Mathematical Society 1976

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