Geodesic
A note on loops of square-free order
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 1, pp. 1-3.

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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.
Classification : 20D15, 20N05
Keywords: loop; inner mapping group; centrally nilpotent loop 
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Leppälä, Emma; Niemenmaa, Markku. A note on loops of square-free order. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 1, pp. 1-3. http://geodesic.mathdoc.fr/item/CMUC_2013__54_1_a0/