| Title:
|
On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^4$ (English) |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
559-563 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^4$ are centrally nilpotent of class at most two. (English) |
| Keyword:
|
loop |
| Keyword:
|
inner mapping group |
| MSC:
|
20D10 |
| MSC:
|
20K01 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1211.20065 |
| idMR:
|
MR2858260 |
| . |
| Date available:
|
2010-11-30T16:15:48Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140837 |
| . |
| 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] Csörgö P.: On connected transversals to abelian subgroups and loop theoretical consequences.Arch. Math. (Basel) 86 (2006), 6 499–516. Zbl 1113.20055, MR 2241599, 10.1007/s00013-006-1379-5 |
| Reference:
|
[3] Csörgö P.: Abelian inner mappings and nilpotency class greater than two.European J. Combin. 28 (2007), 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), 7 1662–1681. Zbl 1168.20031, MR 2431758, 10.1016/j.ejc.2007.10.001 |
| Reference:
|
[5] 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:
|
[6] Kepka T., Niemenmaa M.: On connected transversals to abelian subgroups in finite groups.Bull. London Math. Soc. 24 (1992), 343–346. Zbl 0793.20064, MR 1165376, 10.1112/blms/24.4.343 |
| Reference:
|
[7] Kepka T., Niemenmaa M.: On connected transversals to abelian subgroups.Bull. Australian Math. Soc. 49 (1994), 121–128. Zbl 0799.20020, MR 1262682, 10.1017/S0004972700016166 |
| Reference:
|
[8] Kinyon M.: private communication.2009. |
| Reference:
|
[9] Niemenmaa M.: On finite loops whose inner mapping groups are abelian II.Bull. Australian Math. Soc. 71 (2005), 487–492. Zbl 1080.20061, MR 2150938, 10.1017/S0004972700038491 |
| Reference:
|
[10] Niemenmaa M., Rytty M.: Connected transversals and multiplication groups of loops.Quasigroups and Related Systems 15 (2007), 95–107. Zbl 1133.20009, MR 2379127 |
| . |
