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F-quasigroups isotopic to groups

Tomaš Kepka·Michael K. Kinyon·J. D. Phillips
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Abstract

In 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.

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Tomaš Kepka, Michael K. Kinyon, J. D. Phillips. 2006-01-04. F-quasigroups isotopic to groups. https://arxiv.org/abs/math/0601077

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