4-Transitivity and 6-Figures in Finite Klingenberg Planes of Parameters (p2k−1, p)

In this paper, we carry over some of the results which are valid on a certain class of Moufang-Klingenberg planes M(A) coordinatized by an local alternative ring A := A(ε) = A+Aε of dual numbers to finite projective Klingenberg plane M(A) obtained by taking local ring Zq (where prime power q = pk) instead of A. So, we show that the collineation group of M(A) acts transitively on 4-gons, and that any 6-figure corresponds to only one inversible m ∈ A.

Authors:

• Atilla Akpinar
• Basri Celik
• Suleyman Ciftci

Keywords:

• finite Klingenberg plane
• projective collineation
• 4-transitivity
• 6-figures.

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