A construction of loops by means of regular permutation sets

Following the slid product construction for loops with inverses of [Pasotti, S. and E. Zizioli, Loops with two-sided inverses constructed by a class of regular permutation sets, J. Geom. 100 (2011), pp. 129–145. URL http://dx.doi.org/10.1007/s00022-011-0071-5], we present here the general setting ensuring the construction of a new loop ( L , ⊕ ) starting from loops ( K , + ) , ( P , + ˆ ) and ( P , + ) possessing suitable properties. The results established in the aforementioned note are generalized as well. Moreover we investigate the nuclei of L and the normality of subloops isomorphic to ( K , + ) and ( P , + ˆ ) .