Some remarks on Havlíček-Tietze configuration

Abstract

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On Havlíček-Tietze configuration in some non-Desarguesian planes

“…be the pairs of ordered triples. We obtain the points B t = (a 2 , a 2 ), B The triangles with vertices X i9 X 2 , X 3 , A i9 A 2 , A 3 , B u B 2 , B 3 , C iy C 2 , C 3 , together with the respective lines form the H-T configuration in the sense of [4].…”

“…This configuration was examined in detail in [4] and [5]. In particular, in [4] it was proved that in a desarguesian projective plane there exists an H-T configuration if and only if its coordinatizing field contains a root of the polynomial x 2 + x + 1 different from 1. H-T configurations exists also in some non-desarguesian planes, in particular in the translation projective planes of order 16 containing subplanes of order 4 (see [3]).…”