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Article

Leppälä, Emma ; Niemenmaa, Markku
A note on loops of square-free order. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 54 (2013), issue 1, pp. 1-3
MSC: 20D15, 20N05 | MR 3038067
Keywords:
loop; inner mapping group; centrally nilpotent loop
Summary:
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.
References:
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[2] Doerk K., Hawkes T.: Finite Soluble Groups. de Gruyter, Berlin, 1992. MR 1169099 | Zbl 0753.20001
[3] Kepka T., Niemenmaa M.: On multiplication groups of loops. J. Algebra 135 (1990), 112–122. DOI 10.1016/0021-8693(90)90152-E | MR 1076080 | Zbl 0706.20046
[4] Niemenmaa M.: Finite loops with nilpotent inner mapping groups are centrally nilpotent. Bull. Aust. Math. Soc. 79 (2009), no. 1, 109–114. DOI 10.1017/S0004972708001093 | MR 2486887 | Zbl 1167.20039
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