| Title:
|
On quasigroups with the left loop property (English) |
| Author:
|
Issa, A. Nourou |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
663-669 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered. (English) |
| Keyword:
|
quasigroups |
| Keyword:
|
loops |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1051.20032 |
| idMR:
|
MR1800175 |
| . |
| Date available:
|
2009-01-08T19:06:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119200 |
| . |
| Reference:
|
[1] Belousov V.D.: Foundations of the theory of quasigroups and loops (in Russian).Izdat. Nauka, Moscow, 1967. MR 0218483 |
| Reference:
|
[2] Bruck R.H.: Some results in the theory of quasigroups.Trans. Amer. Math. Soc. 55 (1944), 19-52. Zbl 0063.00635, MR 0009963 |
| Reference:
|
[3] Bruck R.H.: A Survey of Binary Systems.Springer-Verlag, Berlin-Gottingen-Heidelberg, 1958. Zbl 0141.01401, MR 0093552 |
| Reference:
|
[4] Fenyves F.: Extra loops II.Publ. Math. Debrecen 16 (1969), 187-192. MR 0262409 |
| Reference:
|
[5] Issa A.N.: Gyrogroups and homogeneous loops.Reports Math. Phys. 44 (1999), 3 345-357. Zbl 0953.20055, MR 1737383 |
| Reference:
|
[6] Kepka T.: Commutative Moufang loops and distributive Steiner quasigroups nilpotent of class $3$.Comment. Math. Univ. Carolinae 21 (1980), 355-370. Zbl 0439.20048, MR 0580690 |
| Reference:
|
[7] Kikkawa M.: Geometry of homogeneous Lie loops.Hiroshima Math. J. 5 (1975), 141-179. Zbl 0304.53037, MR 0383301 |
| Reference:
|
[8] Kunen K.: Moufang quasigroups.J. Algebra 183 (1996), 231-234. Zbl 0855.20056, MR 1397396 |
| Reference:
|
[9] Kunen K.: Quasigroups, loops, and associative laws.J. Algebra 185 (1996), 194-204. Zbl 0860.20053, MR 1409983 |
| Reference:
|
[10] Pflugfelder H.O.: Quasigroups and Loops: Introduction.Heldermann, Berlin, 1990. Zbl 0715.20043, MR 1125767 |
| Reference:
|
[11] Robinson D.A.: Bol loops.Trans. Amer. Math. Soc. 123 (1966), 341-354. Zbl 0163.02001, MR 0194545 |
| Reference:
|
[12] Robinson D.A.: Bol quasigroups.Publ. Math. Debrecen 19 (1972), 151-153. MR 0325829 |
| Reference:
|
[13] Sabinin L.V.: On the gyrogroups of Ungar.Russian Math. Surveys 50 (1995), 5 1095-1096. Zbl 0865.20054, MR 1365062 |
| Reference:
|
[14] Sabinin L.V., Mikheev P.O.: On the law of composition of velocities in special relativity theory.Russian Math. Surveys 48 (1993), 5 183-185. Zbl 0814.53057, MR 1258774 |
| Reference:
|
[15] Ungar A.A.: Thomas rotation and the parametrization of the Lorentz transformation group.Foundations Phys. Lett. 1 (1988), 1 57-89. MR 0962332 |
| Reference:
|
[16] Ungar A.A.: Thomas precession and its associated grouplike structure.Amer. J. Phys. 59 (1991), 9 824-834. MR 1126776 |
| . |
