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,+') 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,+').
A construction of loops by means of regular permutation sets
PASOTTI, Stefano;ZIZIOLI, Elena
2013-01-01
Abstract
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,+') 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,+').File in questo prodotto:
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