4-Transitivity and 6-figures in some Moufang-Klingenberg planes
MONATSHEFTE FUR MATHEMATIK, vol.152, no.4, pp.283-294, 2007 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 152 Issue: 4
- Publication Date: 2007
- Doi Number: 10.1007/s00605-007-0477-1
- Journal Name: MONATSHEFTE FUR MATHEMATIK
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.283-294
- Keywords: Moufang-Klingenberg plane, 4-transitivity, projective collineation
- Bursa Uludag University Affiliated: Yes
Abstract
In this paper, the Moufang-Klingenberg plane over a local alternative ring R of dual numbers is studied. It is shown that its collineation group is transitive on quadrangles. It is therefore shown that the coordinatization of these Moufang-Klingenberg planes is independent of the choice of the coordinatization quadrangle. Also, the concept of 6-figures is extended to these Moufang-Klingenberg planes and it is shown that any 6-figure corresponds to only one inversible m epsilon R.