| Title:
|
Nonsplitting F-quasigroups (English) |
| Author:
|
Gagola III, Stephen |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
375-381 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
T. Kepka, M.K. Kinyon and J.D. Phillips: The structure of F-quasigroups, J. Algebra 317 (2007), no. 2, 435--461 developed a connection between F-quasigroups and NK-loops. Since NK-loops are contained in the variety generated by groups and commutative Moufang loops, a question that arises is whether or not there exists a nonsplit NK-loop and likewise a nonsplit F-quasigroup. Here we prove that there do indeed exist nonsplit F-quasigroups and show that there are exactly four corresponding nonsplit NK-loops of minimal order $3^6$. (English) |
| Keyword:
|
F-quasigroup |
| Keyword:
|
NK-loop |
| Keyword:
|
Moufang loop |
| MSC:
|
20E10 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1257.20068 |
| idMR:
|
MR3017836 |
| . |
| Date available:
|
2012-08-31T11:36:41Z |
| Last updated:
|
2014-10-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142930 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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