F-quasigroups isotopic to groups
Tomáš Kepka; Michael K. Kinyon; Jon D. Phillips
Commentationes Mathematicae Universitatis Carolinae (2010)
- Volume: 51, Issue: 2, page 267-277
- ISSN: 0010-2628
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topKepka, Tomáš, Kinyon, Michael K., and Phillips, Jon D.. "F-quasigroups isotopic to groups." Commentationes Mathematicae Universitatis Carolinae 51.2 (2010): 267-277. <http://eudml.org/doc/37759>.
@article{Kepka2010,
abstract = {In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, 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.},
author = {Kepka, Tomáš, Kinyon, Michael K., Phillips, Jon D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {F-quasigroup; Moufang loop; generalized modules; F-quasigroups; Moufang loops; loop isotopes; identities; generalized modules},
language = {eng},
number = {2},
pages = {267-277},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {F-quasigroups isotopic to groups},
url = {http://eudml.org/doc/37759},
volume = {51},
year = {2010},
}
TY - JOUR
AU - Kepka, Tomáš
AU - Kinyon, Michael K.
AU - Phillips, Jon D.
TI - F-quasigroups isotopic to groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 2
SP - 267
EP - 277
AB - In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, 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.
LA - eng
KW - F-quasigroup; Moufang loop; generalized modules; F-quasigroups; Moufang loops; loop isotopes; identities; generalized modules
UR - http://eudml.org/doc/37759
ER -
References
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