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Divisible semibiplanes and conics of Desarguesian biaffine planes. (English) Zbl 0549.51007
A biaffine plane is the incidence structure obtained by deleting all points on a given line \(\ell\) and all lines through a given point P on \(\ell\) from a projective plane. The biaffine plane is said to be Desarguesian if the projective plane is Desarguesian. A semibiplane is a connected incidence structure of a pair of distinct points always belong to either 0 or 2 blocks. The author studies semibiplanes constructed from collections of conics in Desarguesian planes. The automorphism group is very small if the plane has odd order. For even order, there is a surprising connection with some of Knuth’s semifields.
Reviewer: T.G.Ostrom

51E30 Other finite incidence structures (geometric aspects)
51E20 Combinatorial structures in finite projective spaces
05B30 Other designs, configurations
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures