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 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.
Abstract: In this paper we are interested in Moufang-Klingenberg
planesM(A) defined over a local alternative ring A of dual numbers.
We show that some collineations of M(A) preserve cross-ratio.
Abstract: In this paper, we deal with finite projective Klingenberg plane M (A) coordinatized by local ring A := Zq+Zq E (where prime power q = p', e0 Z q and 62 = 0). So, we get some combinatorical results on 6-figures. For example, we show that there exist p — 1 6-figure classes in M(A).
Abstract: In this paper we are interested in Moufang-Klingenberg
planesM(A) defined over a local alternative ring A of dual numbers.
We introduce two new collineations of M(A).
Abstract: In this paper we are interested in Moufang-Klingenberg
planesM(A) defined over a local alternative ring A of dual numbers.
We show that a collineation of M(A) preserve cross-ratio. Also, we
obtain some results about harmonic points.
Abstract: In this paper, the notion of Hyperbolic Klingenberg
plane is introduced via a set of axioms like as Affine Klingenberg
planes and Projective Klingenberg planes. Models of such planes are
constructed by deleting a certain number m of equivalence classes
of lines from a Projective Klingenberg plane. In the finite case, an
upper bound for m is established and some combinatoric properties
are investigated.