Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
loop; multiplication group; inner permutation; $H$-connected transversals
loop; multiplication group; inner permutation; $H$-connected transversals
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.
References:
[1] Bruck R.H.: Contributions to the theory of loops. Trans. Amer. Math. Soc. 60 (1946), 245-354. MR 0017288 | Zbl 0061.02201
[2] Drápal A., Kepka T.: Multiplication groups of quasigroups and loops I. Acta Univ. Carol. Math. Phys. 34 /1 (1993), 85-99. MR 1282769
[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
[4] Kepka T.: Multiplication groups of some quasigroups. Colloq. Math. Soc. J. Bolyai 29 (1977), 459-465. MR 0660883
[5] Kepka T.: On the abelian inner permutation groups of loops. Comm. Algebra 26 (1998), 857-861. MR 1606178 | Zbl 0913.20043
[6] Kepka T., Niemenmaa M.: On loops with cyclic inner mapping groups. Arch. Math. 60 (1993), 233-236. MR 1201636
[7] Kepka T., Phillips J.D.: Connected transversals to subnormal subgroups. Comment. Math. Univ. Carolinae 38 (1997), 223-230. MR 1455488 | Zbl 0889.20020
[8] Niemenmaa M., Kepka T.: On multiplication groups of loops. J. Algebra 135 (1990), 112-122. MR 1076080 | Zbl 0706.20046
[9] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups in finite groups. Bull. London Math. Soc. 24 (1992), 343-346. MR 1165376 | Zbl 0793.20064
[10] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups. Bull. Austral. Math. Soc. 49 (1994), 121-128. MR 1262682 | Zbl 0799.20020
[11] Niemenmaa M.: On the structure of the inner mapping groups of loops. Comm. Algebra 24 (1996), 135-142. MR 1370527 | Zbl 0853.20049
[12] Niemenmaa M.: On finite loops whose inner mapping groups are abelian. Bull. Austral. Math. Soc. 65 (2002), 477-484. MR 1910500 | Zbl 1012.20068
[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. MR 1751102 | Zbl 0954.20039
[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. MR 1780883 | Zbl 1038.20055
[15] Vesanen A.: Solvable loops and groups. J. Algebra 180 (1996), 862-876. MR 1379214
Search
Partner of
