Geodesic
Commutative subloop-free loops
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 473-484.

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We describe, in a constructive way, a family of commutative loops of odd order, $n\geq 7$, which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group $\mathcal{A}_n$.
Classification : 20D06, 20N05
Keywords: loops; multiplication group; alternating group 
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Beaudry, Martin; Marchand, Louis. Commutative subloop-free loops. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 473-484. http://geodesic.mathdoc.fr/item/CMUC_2011__52_4_a0/