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Congruence-Preserving Isomorphisms of the Translation Group associated with a Translation Plane

Published online by Cambridge University Press:  20 November 2018

F. Radó
F. Radó*
Affiliation:
University of Waterloo, Waterloo, Ontario
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Let II, II′ be projective translation planes, their sets of points, l∞, l∞′ the improper lines, and T, T′ the corresponding translation groups. T is an Abelian group, simply transitive on . The set of the subgroups Ts = {τ|τ ∈ T, cen τ = S} for all S ∈ l∞ is called the congruence of II (cen τ = centre of τ). An injective map , where , is said to be a collineation of when and three points in are collinear if and only if their images are collinear; the set of these φ is denoted by and for we write

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 2 , April 1971 , pp. 214 - 221
Copyright
Copyright © Canadian Mathematical Society 1971

References

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