Abstract
In 1944, R. H. Bruck has described a very general construction method which he called the extension of a set by a quasigroup. We use it to construct a class of examples for LF-quasigroups in which the image of the map $e(x) = x\backslash x$ is a group. More generally, we consider the variety of quasigroups which is defined by the property that the map $e$ is an endomorphism and its subvariety where the image of the map $e$ is a group. We characterize quasigroups belonging to these varieties using their Bruck decomposition with respect to the map $e$.
Citation
Péter T. Nagy. Peter Plaumann. "Bruck decomposition for endomorphisms of quasigroups." J. Gen. Lie Theory Appl. 3 (3) 191 - 196, August 2009. https://doi.org/10.4303/jglta/S090305
Information