| Title:
|
On loops whose inner permutations commute (English) |
| Author:
|
Csörgö, Piroska |
| Author:
|
Kepka, Tomáš |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
213-221 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Multiplication groups of (finite) loops with commuting inner permutations are investigated. Special attention is paid to the normal closure of the abelian permutation group. (English) |
| Keyword:
|
loop |
| Keyword:
|
multiplication group |
| Keyword:
|
inner permutation |
| Keyword:
|
$H$-connected transversals |
| MSC:
|
20D10 |
| MSC:
|
20D40 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1101.20034 |
| idMR:
|
MR2075270 |
| . |
| Date available:
|
2009-05-05T16:44:36Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119451 |
| . |
| 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] Drápal A., Kepka T.: Multiplication groups of quasigroups and loops I.Acta Univ. Carol. Math. Phys. 34 /1 (1993), 85-99. MR 1282769 |
| Reference:
|
[3] Drápal A., Kepka T., Maršálek O.: Multiplication groups of quasigroups and loops II.Acta Univ Carol. Math. Phys. 35 /1 (1994), 9-29. MR 1366489 |
| Reference:
|
[4] Kepka T.: Multiplication groups of some quasigroups.Colloq. Math. Soc. J. Bolyai 29 (1977), 459-465. MR 0660883 |
| Reference:
|
[5] Kepka T.: On the abelian inner permutation groups of loops.Comm. Algebra 26 (1998), 857-861. Zbl 0913.20043, MR 1606178 |
| Reference:
|
[6] Kepka T., Niemenmaa M.: On loops with cyclic inner mapping groups.Arch. Math. 60 (1993), 233-236. MR 1201636 |
| Reference:
|
[7] Kepka T., Phillips J.D.: Connected transversals to subnormal subgroups.Comment. Math. Univ. Carolinae 38 (1997), 223-230. Zbl 0889.20020, MR 1455488 |
| Reference:
|
[8] Niemenmaa M., Kepka T.: On multiplication groups of loops.J. Algebra 135 (1990), 112-122. Zbl 0706.20046, MR 1076080 |
| Reference:
|
[9] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups in finite groups.Bull. London Math. Soc. 24 (1992), 343-346. Zbl 0793.20064, MR 1165376 |
| Reference:
|
[10] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups.Bull. Austral. Math. Soc. 49 (1994), 121-128. Zbl 0799.20020, MR 1262682 |
| Reference:
|
[11] Niemenmaa M.: On the structure of the inner mapping groups of loops.Comm. Algebra 24 (1996), 135-142. Zbl 0853.20049, MR 1370527 |
| Reference:
|
[12] Niemenmaa M.: On finite loops whose inner mapping groups are abelian.Bull. Austral. Math. Soc. 65 (2002), 477-484. Zbl 1012.20068, MR 1910500 |
| Reference:
|
[13] Phillips J.D.: A note on simple groups and simple loops.in: Proc. of the Groups (Korea, 1998), W. de Gruyter, Berlin, 2000, pp.305-317. Zbl 0954.20039, MR 1751102 |
| Reference:
|
[14] Smith J.D.J.: Loops and quasigroups: aspects of current work and prospects for the future.Comment. Math. Univ. Carolinae 41 (2000), 415-427. Zbl 1038.20055, MR 1780883 |
| Reference:
|
[15] Vesanen A.: Solvable loops and groups.J. Algebra 180 (1996), 862-876. MR 1379214 |
| . |
