Geodesic
On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2009), pp. 52-56 
Natalia Lupashco. On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2009), pp. 52-56. http://geodesic.mathdoc.fr/item/BASM_2009_3_a4/
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     title = {On commutative {Moufang} loops with some restrictions for subloops and subgroups of its multiplication groups},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that if an infinite commutative Moufang loop $L$ has such an infinite subloop $H$ that in $L$ every associative subloop which has with $H$ an infinite intersection is a normal subloop then the loop $L$ is associative. It is also proved that if the multiplication group $\mathfrak M$ of infinite commutative Moufang loop $L$ has such an infinite subgroup $\mathfrak N$ that in $\mathfrak M$ every abelian subgroup which has with $\mathfrak N$ an infinite intersection is a normal subgroup then the loop $L$ is associative.

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