| Title:
|
On finite commutative loops which are centrally nilpotent (English) |
| Author:
|
Leppälä, Emma |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
139-143 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $Q$ be a finite commutative loop and let the inner mapping group $I(Q) \cong C_{p^n} \times C_{p^n}$, where $p$ is an odd prime number and $n \geq 1$. We show that $Q$ is centrally nilpotent of class two. (English) |
| Keyword:
|
loop |
| Keyword:
|
inner mapping group |
| Keyword:
|
centrally nilpotent loop |
| MSC:
|
20D15 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 06433813 |
| idMR:
|
MR3338728 |
| DOI:
|
10.14712/1213-7243.2015.113 |
| . |
| Date available:
|
2015-04-25T16:57:00Z |
| Last updated:
|
2017-08-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144236 |
| . |
| Reference:
|
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| Reference:
|
[2] Csörgö P.: Abelian inner mappings and nilpotency class greater than two.European J. Combin. 28 (2007), 858–867. Zbl 1149.20053, MR 2300766, 10.1016/j.ejc.2005.12.002 |
| Reference:
|
[3] Drápal A., Vojtěchovský P.: Explicit constructions of loops with commuting inner mappings.European J. Combin. 29 (2008), no. 7, 1662–1681. MR 2431758, 10.1016/j.ejc.2007.10.001 |
| Reference:
|
[4] Kepka T., Niemenmaa M.: On loops with cyclic inner mapping groups.Arch. Math. 60 (1993), 233–236. MR 1201636, 10.1007/BF01198806 |
| Reference:
|
[5] Niemenmaa M.: On finite loops whose inner mapping groups are abelian II.Bull. Austral. Math. Soc. 71 (2005), 487–492. Zbl 1080.20061, MR 2150938, 10.1017/S0004972700038491 |
| Reference:
|
[6] Niemenmaa M., Kepka T.: On multiplication groups of loops.J. Algebra 135 (1990), 112–122. Zbl 0706.20046, MR 1076080, 10.1016/0021-8693(90)90152-E |
| Reference:
|
[7] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups.Bull. Austral. Math. Soc. 49 (1994), 121–128. Zbl 0799.20020, MR 1262682, 10.1017/S0004972700016166 |
| Reference:
|
[8] Niemenmaa M., Rytty M.: Connected transversals and multiplication groups of loops.Quasigroups and Related Systems 15 (2007), 95–107. Zbl 1133.20009, MR 2379127 |
| . |
