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Some combinatorial properties of conics in the Hjelmslev plane. (English) Zbl 0853.05018
Summary: We prove some combinatorial properties of conics in desarguesian Hjelmslev planes. The results generalize analogous properties of conics in finite projective geometries, see E. J. F. Primrose [Proc. Cambridge Philos. Soc. 47, 299-304 (1951; Zbl 0042.38803)].

##### MSC:
 05B25 Combinatorial aspects of finite geometries 51D99 Geometric closure systems
##### Keywords:
conics; desarguesian Hjelmslev planes
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##### References:
 [1] BOSE R. C, CHAKRAVARTI I. M.: Hermitian Varieties in a Finite Projective Space PG N, $$q^2$$. Lecture Notes, Chapel Hill., N.C. · Zbl 0163.42501 · doi:10.4153/CJM-1966-116-0 [2] CHVÁL V.: Some Properties of Quadratics in Hjelmslev Plane. (Slovak). Technical Report I-4-2/9a, PF UPJŠ, Kosice, 1975. [3] JURGA R.: Some Properties of Quadratics in Hjelmslev Plane. Thesis, PHF EU, Košice, 1990. [4] PRIMROSE E. J. F.: Quadrics in finite geometries. Proc. Cambridge Philos. Soc. 47 (1951), 299-304. · Zbl 0042.38803
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