Finite geometries without the axiom of parallels Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/kh04ds19q

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  • Among the geometries with n points on every line (with n an integer greater than one), those in which there are no parallels and those in which the axiom of parallels holds have been discussed (as finite projective and affine geometries) in the literature. This paper contrasts such geometries with a Bolyai-Lobatchevski finite geometry in which there are at least two parallels to a given line at a point not on that line. Existence theorems for the plane are given, as well as methods of construction and identification of certain Steiner systems as planes. The non-existence of k-spaces is proved when k > 3.
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