| Title:
|
On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^5$ (English) |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
547-551 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^5$ are centrally nilpotent of class at most two. (English) |
| Keyword:
|
loop |
| Keyword:
|
elementary abelian group |
| Keyword:
|
inner mapping group |
| MSC:
|
20D10 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 07332728 |
| idMR:
|
MR4230959 |
| DOI:
|
10.14712/1213-7243.2020.034 |
| . |
| Date available:
|
2021-02-25T12:45:38Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148664 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Csörgö P.: Abelian inner mappings and nilpotency class greater than two.European J. Combin. 28 (2007), no. 3, 858–867. Zbl 1149.20053, MR 2300766, 10.1016/j.ejc.2005.12.002 |
| Reference:
|
[4] 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:
|
[5] Leppälä E., Niemenmaa M.: On finite commutative loops which are centrally nilpotent.Comment. Math. Univ. Carolin. 56 (2015), no. 2, 139–143. Zbl 1339.20064, MR 3338728 |
| Reference:
|
[6] 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 |
| Reference:
|
[7] Niemenmaa M.: On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^4$.Comment. Math. Univ. Carolin. 51 (2010), no. 4, 559–563. MR 2858260 |
| Reference:
|
[8] Niemenmaa M.: On dihedral $2$-groups as inner mapping groups of finite commutative inverse property loops.Comment. Math. Univ. Carolin. 59 (2018), no. 2, 189–193. MR 3815684 |
| Reference:
|
[9] Niemenmaa M., Kepka T.: On multiplication groups of loops.J. Algebra 135 (1990), no. 1, 112–122. Zbl 0706.20046, MR 1076080, 10.1016/0021-8693(90)90152-E |
| Reference:
|
[10] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups.Bull. Austral. Math. Soc. 49 (1994), no. 1, 121–128. Zbl 0799.20020, MR 1262682, 10.1017/S0004972700016166 |
| Reference:
|
[11] Niemenmaa M., Rytty M.: Connected transversals and multiplication groups of loops.Quasigroups Related Systems 15 (2007), no. 1, 95–107. Zbl 1133.20009, MR 2379127 |
| . |
