Doppelebenen und Loops

Generalizing the concept of difference sets in groups conditions are given for a loop (P, +) (with equality of left and right inverses) and a subset D of P such that (i) the left translates of D and the right translates of -D (the set of inverses for elements of D) resp. are the lines of two projective planes with point set P, forming a double plane (i.e. the lines of one plane are ovals of the other), (ii) the loop operation has a certain geometric interpretation in the double plane.

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Walter Benz zum 60. Geburtstag