On loops whose inner permutations commute

Piroska Csörgö; Tomáš Kepka

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 2, page 213-221
  • ISSN: 0010-2628

Abstract

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Multiplication groups of (finite) loops with commuting inner permutations are investigated. Special attention is paid to the normal closure of the abelian permutation group.

How to cite

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Csörgö, Piroska, and Kepka, Tomáš. "On loops whose inner permutations commute." Commentationes Mathematicae Universitatis Carolinae 45.2 (2004): 213-221. <http://eudml.org/doc/249358>.

@article{Csörgö2004,
abstract = {Multiplication groups of (finite) loops with commuting inner permutations are investigated. Special attention is paid to the normal closure of the abelian permutation group.},
author = {Csörgö, Piroska, Kepka, Tomáš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; multiplication group; inner permutation; $H$-connected transversals; loops; connected transversals; Abelian inner mapping groups; multiplication groups},
language = {eng},
number = {2},
pages = {213-221},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On loops whose inner permutations commute},
url = {http://eudml.org/doc/249358},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Csörgö, Piroska
AU - Kepka, Tomáš
TI - On loops whose inner permutations commute
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 2
SP - 213
EP - 221
AB - Multiplication groups of (finite) loops with commuting inner permutations are investigated. Special attention is paid to the normal closure of the abelian permutation group.
LA - eng
KW - loop; multiplication group; inner permutation; $H$-connected transversals; loops; connected transversals; Abelian inner mapping groups; multiplication groups
UR - http://eudml.org/doc/249358
ER -

References

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  3. Drápal A., Kepka T., Maršálek O., Multiplication groups of quasigroups and loops II, Acta Univ Carol. Math. Phys. 35 /1 (1994), 9-29. (1994) MR1366489
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  10. Niemenmaa M., Kepka T., On connected transversals to abelian subgroups, Bull. Austral. Math. Soc. 49 (1994), 121-128. (1994) Zbl0799.20020MR1262682
  11. Niemenmaa M., On the structure of the inner mapping groups of loops, Comm. Algebra 24 (1996), 135-142. (1996) Zbl0853.20049MR1370527
  12. Niemenmaa M., On finite loops whose inner mapping groups are abelian, Bull. Austral. Math. Soc. 65 (2002), 477-484. (2002) Zbl1012.20068MR1910500
  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. Zbl0954.20039MR1751102
  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. (2000) Zbl1038.20055MR1780883
  15. Vesanen A., Solvable loops and groups, J. Algebra 180 (1996), 862-876. (1996) MR1379214

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