4-Transitivity and 6-figures in finite klingenberg planes of parameters (p2k-1, p)

Abstract

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 Z<inf>q</inf> (where prime power q = p^k) 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.