Semidirect Product of Loops and Fibrations

. Starting from two loops ( H , +) and ( K , ·), a new loop L can be defined by means of a suitable map Θ : K → Sym H (cf. [3]). Such a loop is called semidirect product of H and K with respect to Θ and denoted by H × Θ K =: L . Here we consider the class of those semidirect products in which Θ : K → Aut( H , +) is a homomorphism, this situation being quite akin to the group case. Some relevant algebraic properties of the loop L (Bol condition, Moufang etc.) can be inherited from H and K . In the case that K is a group we investigate the possibility of describing L by a partition (or fibration). In this way we propose a generalization of [8] for the non associative case.