Abstract.
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Helmut Karzel on the occasion of his 80th birthday
This research is supported by M.I.U.R.
Received: September 20, 2007. Revised: November 8, 2007.
Rights and permissions
About this article
Cite this article
Zizioli, E. Semidirect Product of Loops and Fibrations. Result. Math. 51, 373–382 (2008). https://doi.org/10.1007/s00025-007-0284-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-007-0284-y