Finite Hjelmslev planes with new integer invariants
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Projective Hjelmslev planes (PH-planes) are a generalization of projective planes in which each point-pair is joined by at least one line and, dually, each line-pair has a nontrivial intersection. Multiply joined points (and multiply inter secting lines) are called neighbor points (and neighbor lines). By hypothesis, the neighbor relations of a PH-plane A are equivalence relations which induce a can onical epimorphism from A to a projective plane A If A is finite, there exists [4] an integer t such that the inverse image of every point and every line of A contains precisely t 2 elements. If the order of A is r, we say that A is a (t, r) PH-plane. We are concerned with the problem of determining the spectrum S of all admissible pairs (t, r). Since the finite projective planes are simply the (1, r) PH-planes, our concern is with a generalization of the classical existence question for projective planes.
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