4-Transitivity and Cross-Ratio in Moufang-Klingenberg Planes over Rings of Plural Numbers

F. O. Erdoǧan ()
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F. O. Erdoǧan: University of Uludaǧ

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1417-1432

Abstract: 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.

Keywords: local ring; Moufang-Klingenberg plane; 4-transitivity; projective collineation; cross-ratio; 51A35; 51A10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0474-9

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