| Title:
|
Realizations of Loops and Groups defined by short identities (English) |
| Author:
|
Keedwell, A. D. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
373-383 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In a recent paper, those quasigroup identities involving at most three variables and of “length” six which force the quasigroup to be a loop or group have been enumerated by computer. We separate these identities into subsets according to what classes of loops they define and also provide humanly-comprehensible proofs for most of the computer-generated results. (English) |
| Keyword:
|
quasigroup identity |
| Keyword:
|
loop |
| Keyword:
|
group |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1204.20084 |
| idMR:
|
MR2573411 |
| . |
| Date available:
|
2009-09-23T21:34:35Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134910 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/137454 |
| . |
| Reference:
|
[1] Belousov V.D.: Balanced identities in quasigroups.(in Russian), Mat. Sb. (N.S.) 70 (112) (1966), 55--97. Zbl 0199.05203, MR 0202898 |
| Reference:
|
[2] Belousov V.D.: A theorem on balanced identities.(in Russian), Mat. Issled. 71 (1983), 22--24. Zbl 0544.20060, MR 0699119 |
| Reference:
|
[3] Fiala N.C.: Short identities implying that a quasigroup is a loop or group.Quasigroups Related Systems 15 (2007), 263--271. MR 2383952 |
| Reference:
|
[4] Sade A.: Entropie demosienne de multigroupoïdes et de quasigroupes.Ann. Soc. Sci. Bruxelles, Sér. I, 73 (1959), 302--309. Zbl 0092.25804, MR 0124255 |
| Reference:
|
[5] Taylor M.A.: A generalization of a theorem of Belousov.Bull. Lond. Math. Soc. 10 (1978), 285--286. Zbl 0408.20056, MR 0519910, 10.1112/blms/10.3.285 |
| . |
