Geodesic
F-quasigroups isotopic to groups
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 267-277

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In Kepka T., Kinyon M.K., Phillips J.D., {\it The structure of F-quasigroups\/}, {\tt math.GR/0510298}, 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 FG-quasigroups. 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.
Classification : 16Y99, 17A30, 20N05
Keywords: F-quasigroup; Moufang loop; generalized modules 
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     title = {F-quasigroups isotopic to groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {267--277},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2010__51_2_a11/}
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Kepka, Tomáš; Kinyon, Michael K.; Phillips, J. D. F-quasigroups isotopic to groups. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 267-277. http://geodesic.mathdoc.fr/item/CMUC_2010__51_2_a11/