Journal Title/Source
Commentationes Mathematicae Universitatis Carolinae
Publication Date
2010
Volume
51
Page Numbers
267–277
Document Type
Journal Article
Department
Mathematics and Computer Science
Abstract
In [5] we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FGquasigroups. We show that FG-quasigroups are linear over groups. We then use this fact to describe their structure. This gives us, for instance, a complete description of the simple FG-quasigroups. Finally, we show an equivalence of equational classes between pointed FG-quasigroups and central generalized modules over a particular ring.
Recommended Citation
Phillips, J.D., "F-QUASIGROUPS ISOTOPIC TO GROUPS" (2010). Journal Articles. 517.
https://commons.nmu.edu/facwork_journalarticles/517