| Title:
|
F-quasigroups isotopic to groups (English) |
| Author:
|
Kepka, Tomáš |
| Author:
|
Kinyon, Michael K. |
| Author:
|
Phillips, J. D. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
267-277 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
F-quasigroup |
| Keyword:
|
Moufang loop |
| Keyword:
|
generalized modules |
| MSC:
|
16Y99 |
| MSC:
|
17A30 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1211.20062 |
| idMR:
|
MR2682480 |
| . |
| Date available:
|
2010-05-21T12:48:19Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140106 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Kepka T.: F-quasigroups isotopic to Moufang loops.Czechoslovak Math. J. 29(104) (1979), no. 1, 62–83. Zbl 0444.20067, MR 0518141 |
| Reference:
|
[5] Kepka T., Kinyon M.K., Phillips J.D.: The structure of F-quasigroups.math.GR/0510298. Zbl 1133.20051 |
| Reference:
|
[6] Kepka T., Kinyon M.K., Phillips J.D.: F-quasigroups and generalized modules.math.GR/0512244. |
| Reference:
|
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| Reference:
|
[8] Pflugfelder H.: Quasigroups and Loops: Introduction.Sigma Series in Pure Math. 8, Helderman, Berlin, 1990. Zbl 0715.20043, MR 1125767 |
| Reference:
|
[9] Sabinina L.L.: On the theory of $F$-quasigroups.in Webs and Quasigroups, pp. 127–130, Kalinin. Gos. Univ., Kalinin, 1988. Zbl 0681.20044, MR 0949717 |
| . |
