Automorphisms of Commutative Moufang Loops Satisfying the Minimality Condition

We consider commutative Moufang loops $Q$ with multiplicative group $\mathfrak{M}$ satisfying the minimality condition for its subloops. Such loops, as well as the class of such loops, are characterized by various subgroups of automorphism groups $\operatorname{Aut}Q$ and $\operatorname{Aut}\mathfrak{M}$. We study the structure of the groups $\operatorname{Aut}Q$ and $\operatorname{Aut}\mathfrak{M}$ and prove that these groups have matrix representations.