Open Access
August 2009 Bruck decomposition for endomorphisms of quasigroups
Péter T. Nagy, Peter Plaumann
J. Gen. Lie Theory Appl. 3(3): 191-196 (August 2009). DOI: 10.4303/jglta/S090305


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 $e$.


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Péter T. Nagy. Peter Plaumann. "Bruck decomposition for endomorphisms of quasigroups." J. Gen. Lie Theory Appl. 3 (3) 191 - 196, August 2009.


Published: August 2009
First available in Project Euclid: 6 August 2010

zbMATH: 1179.20062
MathSciNet: MR2534024
Digital Object Identifier: 10.4303/jglta/S090305

Primary: 20N05

Keywords: Generalizations of groups , Group theory , loops , Quasigroups

Rights: Copyright © 2009 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • No. 3 • August 2009
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