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
$e$.
Publié le : 2009-08-15
Classification:
Group theory,
Generalizations of groups,
Loops,
Quasigroups,
20N05
@article{1281106538,
author = {Nagy, P\'eter T. and Plaumann, Peter},
title = {Bruck decomposition for endomorphisms of quasigroups},
journal = {J. Gen. Lie Theory Appl.},
volume = {3},
number = {3},
year = {2009},
pages = { 191-196},
language = {en},
url = {http://dml.mathdoc.fr/item/1281106538}
}
Nagy, Péter T.; Plaumann, Peter. Bruck decomposition for endomorphisms of quasigroups. J. Gen. Lie Theory Appl., Tome 3 (2009) no. 3, pp. 191-196. http://gdmltest.u-ga.fr/item/1281106538/