| Title:
|
Selfdistributive groupoids of small orders (English) |
| Author:
|
Ježek, Jaroslav |
| Author:
|
Kepka, Tomáš |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
463-468 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial. (English) |
| Keyword:
|
distributive |
| Keyword:
|
medial |
| Keyword:
|
groupoid |
| MSC:
|
20N02 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 0901.20051 |
| idMR:
|
MR1461425 |
| . |
| Date available:
|
2009-09-24T10:07:20Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127370 |
| . |
| Reference:
|
[1] R. El. Bashir and A. Drápal: Quasitrivial left distributive groupoids.Commentationes Math. Univ. Carolinae 35 (1994), 597–606. MR 1321230 |
| Reference:
|
[2] G. Bol: Gewebe und Gruppen.Math. Ann. 114 (1937), 414–431. Zbl 0016.22603, MR 1513147, 10.1007/BF01594185 |
| Reference:
|
[3] A. Drápal, T. Kepka and M. Musílek: Group conjugation has non-trivial LD-identities.Commentationes Math. Univ. Carolinae 35 (1994), 219–222. MR 1286567 |
| Reference:
|
[4] M. Hall, Jr.: Automorphisms of Steiner triple systems.IBM J. of Research Development 4 (1960), 460–471. Zbl 0100.01803, MR 0123961, 10.1147/rd.45.0460 |
| Reference:
|
[5] J. Ježek and T. Kepka: Atoms in the lattice of varieties of distributive groupoids.Colloquia Math. Soc. J. Bolyai 14. Lattice Theory, Szeged, 1974, pp. 185–194. MR 0485630 |
| Reference:
|
[6] J. Ježek, T. Kepka and P. Němec: Distributive groupoids.Rozpravy ČSAV, Řada mat. a přír. věd 91, Academia, Praha, 1981. MR 0672563 |
| Reference:
|
[7] T. Kepka: .Math. Nachr. 87 (1979), Distributive division groupoids 103–107. Zbl 0444.20067, MR 0536417 |
| Reference:
|
[8] T. Kepka: Notes on quasimodules.Commentationes Math. Univ. Carolinae 20 (1979), 229–247. Zbl 0413.20054, MR 0539554 |
| Reference:
|
[9] T. Kepka and P. Němec: .Czech. Math. J. 31 (1981), Commutative Moufang loops and distributive groupoids of small orders 633–669. MR 0631607 |
| Reference:
|
[10] J. P. Soublin: Étude algébrique de la notion de moyenne.J. Math. Pures et Appl. 50 (1971), 53–264. Zbl 0215.40401, MR 0291342 |
| . |
