| Title:
|
Medial quasigroups of prime square order (English) |
| Author:
|
Stanovský, David |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
585-590 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that, for any prime $p$, there are precisely $2p^4-p^3-p^2-3p-1$ medial quasigroups of order $p^2$, up to isomorphism. (English) |
| Keyword:
|
medial quasigroup |
| Keyword:
|
quasigroup affine over abelian group |
| Keyword:
|
classification of quasigroups |
| Keyword:
|
enumeration of quasigroups |
| MSC:
|
05A15 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 06674899 |
| idMR:
|
MR3583309 |
| DOI:
|
10.14712/1213-7243.2015.181 |
| . |
| Date available:
|
2017-01-09T22:22:28Z |
| Last updated:
|
2019-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145951 |
| . |
| Reference:
|
[1] Drápal A.: Group isotopes and a holomorphic action.Result. Math. 54 (2009), no. 3–4, 253–272. Zbl 1190.20049, MR 2534446, 10.1007/s00025-009-0370-4 |
| Reference:
|
[2] Hou X.: Finite modules over $\mathbb Z[t,t^{-1}]$.J. Knot Theory Ramifications 21 (2012), no. 8, 1250079, 28 pp. MR 2925432 |
| Reference:
|
[3] Hulpke A., Stanovský D., Vojtěchovský P.: Connected quandles and transitive groups.J. Pure Appl. Algebra 220 (2016), no. 2, 735–758. Zbl 1326.57025, MR 3399387, 10.1016/j.jpaa.2015.07.014 |
| Reference:
|
[4] Kirnasovsky O.U.: Linear isotopes of small order groups.Quasigroups Related Systems 2 (1995), no. 1, 51–82. Zbl 0951.20508, MR 1485747 |
| Reference:
|
[5] Macdonald I.G.: Numbers of conjugacy classes in some finite classical groups.Bull. Austral. Math. Soc. 23 (1981), no. 1, 23–48. Zbl 0445.20029, MR 0615131, 10.1017/S0004972700006882 |
| Reference:
|
[6] Sim H.-S., Song H.-J.: Revisit to connected Alexander quandles of small orders via fixed point free automorphisms of finite Abelian groups.East Asian Math. J. 30 (2014), no. 3, 293–302. Zbl 1339.20065, 10.7858/eamj.2014.019 |
| Reference:
|
[7] Sokhatsky F., Syvakivskij P.: On linear isotopes of cyclic groups.Quasigroups Related Systems 1 (1994), no. 1, 66–76. Zbl 0951.20510, MR 1327947 |
| Reference:
|
[8] Stanovský D.: A guide to self-distributive quasigroups, or latin quandles.Quasigroups Related Systems 23 (2015), no. 1, 91–128. Zbl 1328.20085, MR 3353113 |
| Reference:
|
[9] Stanovský D., Vojtěchovský P.: Central and medial quasigroups of small order.Bul. Acad. Ştiinte Repub. Moldova Mat. 80 (2016), no. 1, 24–40. Zbl 1349.20075, MR 3528005 |
| . |
