ar X iv : m at h . G R / 0 60 10 77 v 1 4 J an 2 00 6 F - QUASIGROUPS ISOTOPIC TO GROUPS
نویسنده
چکیده
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.
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تاریخ انتشار 2006