Bruck decomposition for endomorphisms of quasigroups

Details Bruck decomposition for endomorphisms of quasigroups Bruck decomposition for endomorphisms of quasigroups

2009-02-06

arxiv.org/abs/0902.1062v3

Mathematics

Group Theory

to appear in Journal of Generalized Lie Theory and Applications

Scientific paper

In the year 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 $e$.

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