Geodesic
On Frattini subloops and normalizers of commutative Moufang loops
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2012), pp. 16-27 
N. I. Sandu. On Frattini subloops and normalizers of commutative Moufang loops. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2012), pp. 16-27. http://geodesic.mathdoc.fr/item/BASM_2012_3_a1/
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     title = {On {Frattini} subloops and normalizers of commutative {Moufang} loops},
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     url = {http://geodesic.mathdoc.fr/item/BASM_2012_3_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $L$ be a commutative Moufang loop (CML) with the multiplication group $\mathfrak M$, and let $\mathfrak F(L)$, $\mathfrak F(\mathfrak M)$ be the Frattini subloop of $L$ and Frattini subgroup of $\mathfrak M$. It is proved that $\mathfrak F(L)=L$ if and only if $\mathfrak F(\mathfrak M)=\mathfrak M$, and the structure of this CML is described. The notion of normalizer for subloops in CML is defined constructively. Using this it is proved that if $\mathfrak F(L)\neq L$, then $L$ satisfies the normalizer condition and that any divisible subgroup of $\mathfrak M$ is an abelian group and serves as a direct factor for $\mathfrak M$.

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