4-Transitivity and cross-ratio in Moufang-Klingenberg planes over rings of plural numbers

FO Erdoǧan - Indian Journal of Pure and Applied Mathematics, 2020 - Springer
Indian Journal of Pure and Applied Mathematics, 2020Springer
In this paper, we carry the obtained results for a certain class of Moufang-Klingenberg
planes co-ordinatized by the local alternative ring of dual numbers, over to a class of
Moufang-Klingenberg planes coordinatized by the plural algebra of order m which is a local
alternative ring. So, we show that its collineation group is transitive on quadrangles and
therefore that coordinatization of the planes is independent of the choice of the
coordinatization quadrangle. Moreover, by a conjugacy class we discuss the definition of …
Abstract
In this paper, we carry the obtained results for a certain class of Moufang-Klingenberg planes co-ordinatized by the local alternative ring of dual numbers, over to a class of Moufang-Klingenberg planes coordinatized by the plural algebra of order m which is a local alternative ring. So, we show that its collineation group is transitive on quadrangles and therefore that coordinatization of the planes is independent of the choice of the coordinatization quadrangle. Moreover, by a conjugacy class we discuss the definition of cross-ratio of four distinct points on the projective lines for the planes.
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