K-loops derived from Frobenius groups

We consider a generalization of the representation of the so-called co-Minkowski plane (due to H. and R. Struve) to an abelian group (V;+) and a commutative subgroup G of Aut(V;+). If P = G × V satis7es suitable conditions then an invariant re8ection structure (in the sense of Karzel (Discrete Math. 208=209 (1999) 387–409)) can be introduced in P which carries the algebraic structure of K-loop on P (cf. Theorem 1). We investigate the properties of the K-loop (P;+) and its connection with the semi-direct product of V and G. If G is a 7xed point free automorphism group then it is possible to introduce in (P;+) an incidence bundle in such a way that the K-loop (P;+) becomes an incidence 7bered loop (in the sense of Zizioli (J. Geom. 30 (1987) 144–151)) (cf. Theorem 3). c © 2002 Published by Elsevier Science B.V.