Geodesic
On commutative Moufang loops with some restrictions for subgroups of its multiplication groups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2006), pp. 95-101 
N. T. Lupashco. On commutative Moufang loops with some restrictions for subgroups of its multiplication groups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2006), pp. 95-101. http://geodesic.mathdoc.fr/item/BASM_2006_2_a10/
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     title = {On commutative {Moufang} loops with some restrictions for subgroups of its multiplication groups},
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     url = {http://geodesic.mathdoc.fr/item/BASM_2006_2_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathfrak M$ be the multiplication group of a commutative Moufang loop $Q$. In this paper it is proved that if all infinite abelian subgroups of $\mathfrak M$ are normal in $\mathfrak M$, then $Q$ is associative. If all infinite nonabelian subgroups of $\mathfrak M$ are normal in $\mathfrak M$, then all nonassociative subloops of $Q$ are normal in $Q$, all nonabelian subgroups of $\frak M$ are normal in $\mathfrak M$ and the commutator subgroup $\mathfrak M'$ is a finite 3-group.

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