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A Characterization of the Hughes Planes

Published online by Cambridge University Press:  20 November 2018

T. G. Ostrom
T. G. Ostrom*
Affiliation:
Washington State University
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Baer (1) introduced the term "(p,L)-collineation" to denote a central collineation with centre p and axis L. We shall find it convenient to use a modification of the related notion of "(p, L)-transitivity."

Definition. Let π0 be a subplane of the projective plane π. Let L be a fixed line of π0, and let p be a fixed point of π0. Let r and s be any two points of π0 that are collinear with p, distinct from p, and not on L. If, for each such choice of r and s, there is a (p, L)-collineation of π that (1) carries π0 into itself and (2) carries r into s, we shall say that π is (p, L, π0)-transitive.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 916 - 922
Copyright
Copyright © Canadian Mathematical Society 1965

References

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