A note on loops of square-free order

Emma Leppälä; Markku Niemenmaa

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 1, page 1-3
  • ISSN: 0010-2628

Abstract

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Let Q be a loop such that | Q | is square-free and the inner mapping group I ( Q ) is nilpotent. We show that Q is centrally nilpotent of class at most two.

How to cite

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Leppälä, Emma, and Niemenmaa, Markku. "A note on loops of square-free order." Commentationes Mathematicae Universitatis Carolinae 54.1 (2013): 1-3. <http://eudml.org/doc/252541>.

@article{Leppälä2013,
abstract = {Let $Q$ be a loop such that $|Q|$ is square-free and the inner mapping group $I(Q)$ is nilpotent. We show that $Q$ is centrally nilpotent of class at most two.},
author = {Leppälä, Emma, Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {finite loops; inner mapping group; centrally nilpotent loop; multiplication groups; finite loops; inner mapping groups; centrally nilpotent loops; multiplication groups},
language = {eng},
number = {1},
pages = {1-3},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on loops of square-free order},
url = {http://eudml.org/doc/252541},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Leppälä, Emma
AU - Niemenmaa, Markku
TI - A note on loops of square-free order
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 1
SP - 1
EP - 3
AB - Let $Q$ be a loop such that $|Q|$ is square-free and the inner mapping group $I(Q)$ is nilpotent. We show that $Q$ is centrally nilpotent of class at most two.
LA - eng
KW - finite loops; inner mapping group; centrally nilpotent loop; multiplication groups; finite loops; inner mapping groups; centrally nilpotent loops; multiplication groups
UR - http://eudml.org/doc/252541
ER -

References

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  1. Bruck R.H., Contributions to the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245–354. Zbl0061.02201MR0017288
  2. Doerk K., Hawkes T., Finite Soluble Groups, de Gruyter, Berlin, 1992. Zbl0753.20001MR1169099
  3. Kepka T., Niemenmaa M., 10.1016/0021-8693(90)90152-E, J. Algebra 135 (1990), 112–122. Zbl0706.20046MR1076080DOI10.1016/0021-8693(90)90152-E
  4. Niemenmaa M., 10.1017/S0004972708001093, Bull. Aust. Math. Soc. 79 (2009), no. 1, 109–114. Zbl1167.20039MR2486887DOI10.1017/S0004972708001093

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