Extension of a class of fibered loops to kinematic spaces

The notion of the split extension of a commutative kinematic space is extended to the case of a weak K-loop with an incidence fibration (F, +, ). Theorem 1 states conditions under wich the quasi-direct productG F⁺ _Q with Aut(F, +) can be turned in a fibered incidence group (G, , o) such that (F, +, ) becomes embeddable inG, and Theorem 2 the additional assumption such that (G, , o) is even a kinematic space. In section 4, Theorem 3 shows that there are suitable examples of proper K-loops with an incidence fibration (derived from hyperbolic planes) on which one can apply Theorem 2.Dedicated to Erich Ellers on the occasion of his 70th birthdayResearch supported by M.U.R.S.T. 40% and by C.N.R. (G.N.S.A.G.A.)