| Title:
|
A note on loops of square-free order (English) |
| Author:
|
Leppälä, Emma |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
1-3 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $Q$ be a loop such that $|Q|$ is square-free and the inner mapping group $I(Q)$ is nilpotent. We show that $Q$ is centrally nilpotent of class at most two. (English) |
| Keyword:
|
loop |
| Keyword:
|
inner mapping group |
| Keyword:
|
centrally nilpotent loop |
| MSC:
|
20D15 |
| MSC:
|
20N05 |
| idMR:
|
MR3038067 |
| . |
| Date available:
|
2013-02-21T13:57:55Z |
| Last updated:
|
2015-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143146 |
| . |
| Reference:
|
[1] Bruck R.H.: Contributions to the theory of loops.Trans. Amer. Math. Soc. 60 (1946), 245–354. Zbl 0061.02201, MR 0017288 |
| Reference:
|
[2] Doerk K., Hawkes T.: Finite Soluble Groups.de Gruyter, Berlin, 1992. Zbl 0753.20001, MR 1169099 |
| Reference:
|
[3] Kepka T., Niemenmaa M.: On multiplication groups of loops.J. Algebra 135 (1990), 112–122. Zbl 0706.20046, MR 1076080, 10.1016/0021-8693(90)90152-E |
| Reference:
|
[4] Niemenmaa M.: Finite loops with nilpotent inner mapping groups are centrally nilpotent.Bull. Aust. Math. Soc. 79 (2009), no. 1, 109–114. Zbl 1167.20039, MR 2486887, 10.1017/S0004972708001093 |
| . |
