| Title:
|
$m$-medial $n$-quasigroups (English) |
| Author:
|
Kepka, Tomáš |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
9-14 |
| . |
| Category:
|
math |
| . |
| Summary:
|
For $n\geq 4$, every $n$-medial $n$-quasigroup is medial. If $1\leq m<n$, then there exist $m$-medial $n$-quasigroups which are not $(m+1)$-medial. (English) |
| Keyword:
|
$n$-quasigroup |
| Keyword:
|
medial |
| MSC:
|
20N05 |
| MSC:
|
20N15 |
| idZBL:
|
Zbl 0736.20044 |
| idMR:
|
MR1118284 |
| . |
| Date available:
|
2008-10-09T13:10:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116937 |
| . |
| Reference:
|
[1] Bénéteau L.: Free commutative Moufang loops and anticommutative graded rings.J. Algebra 67 (1980), 1-35. MR 0595016 |
| Reference:
|
[2] Bénéteau L.: Une classe particulière de matroïdes parfaits.Annals of Discr. Math. 8 (1980), 229-232. MR 0597178 |
| Reference:
|
[3] Bénéteau L., Kepka t., Lacaze J.: Small finite trimedial quasigroups.Commun. Algebra 14 (1986), 1067-1090. MR 0837271 |
| Reference:
|
[4] Bol G.: Gewebe und Gruppen.Math. Ann. 114 (1937), 414-431. Zbl 0016.22603, MR 1513147 |
| Reference:
|
[5] Deza M., Hamada N.: The geometric structure of a matroid design derived from some commutative Moufang loops and a new MDPB association scheme.Techn. report nr. 18, Statistic Research group, Hiroshima Univ., 1980. |
| Reference:
|
[6] Evans T.: Abstract mean values.Duke Math. J. 30 (1963), 331-347. Zbl 0118.26304, MR 0155781 |
| Reference:
|
[7] Kepka T.: Structure of triabelian quasigroups.Comment. Math. Univ. Carolinae 17 (1976), 229-240. Zbl 0338.20097, MR 0407182 |
| . |
