Semidirect product of loops and fibrations. (Q927821)

The author considers the class of a new loop \(L\), the semidirect product of loops \((H,+)\) and \((K,\cdot)\) with respect to a map \(\Theta\colon K\to\text{Sym\,}H\). In a special case \(\Theta\colon K\to\Aut(H,+)\) is a homomorphism. In the case that \(K\) is a group the author investigates the possibility of describing the loop \(L\) by a fibration. The author proposes a generalization of results of \textit{M. Marchi} and \textit{E. Zizioli} [in Ann. Discrete Math. 18, 601-616 (1993; Zbl 0509.51011)] for the nonassociative case.