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Let $L$ be a commutative Moufang loop (CML) with multiplication group $\frakM$, and let $\frak F(L)$, $\frak F(\frak M)$ be the Frattini subgroup andFrattini subgroup of $L$ and $\frak M$ respectively. It is proved that $\frakF(L) = L$ if and only if $\frak F(\frak M) = \frak M$ and is described thestructure of this CLM. Constructively it is defined the notion of normalizerfor subloops in CML. Using this it is proved that if $\frak F(L) \neq L$ then$L$ satisfies the normalizer condition and that any divisible subgroup of$\frak M$ is an abelian group and serves as a direct factor for $\frak M$.

On Frattini subloops and normalizers of commutative Moufang loops