On Frattini subloops and normalizers of commutative Moufang loops

Let $L$ be a commutative Moufang loop (CML) with multiplication group $\frak M$,andlet$\frak F(L)$,$\frak F(\frak M)$ be the Frattini subgroup and Frattini subgroup of $L$ and $\mathfrak{M}$ respectively. It is proved that $\frak F(L) = L$ifandonlyif$\frak F(\frak M) = \frak M$ and is described the structure of this CLM. Constructively it is defined the notion of normalizer for subloops in CML. Using this it is proved that if $\mathfrak{F}(L)\mathrm{\ne }L$ 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 $\mathfrak{M}$.