F-quasigroups isotopic to groups
群论
2011-08-19 v1
摘要
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.
引用
@article{arxiv.math/0601077,
title = {F-quasigroups isotopic to groups},
author = {Tomaš Kepka and Michael K. Kinyon and J. D. Phillips},
journal= {arXiv preprint arXiv:math/0601077},
year = {2011}
}
备注
11 pages; refers to math.GR/0510298 and math.GR/0512244