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-Homogeneity of Projective Planes and Polarities
Published online by Cambridge University Press: 20 November 2018
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In (1) Baer introduced the concept of (C, γ)-transitivity and (C, γ)- homogeneity. A projective plane (see (5) for the requisite definitions and axioms) is (C, γ)-transitive if, given an ordered pair (P1, P2) of points collinear with C but distinct from C and not on γ, there is a collineation which maps P1 into P2 and leaves fixed every point on γ as well as every line through C. A projective plane is (C, γ)-homogeneous for a non-incident point-line-pair if it is (C, γ) transitive and there is a correlation which maps every line through C into its intersection with γ and every point on γ into its join with C.
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- Copyright © Canadian Mathematical Society 1965