On periodic groups of automorphisms of extremal groups

Abstract

It is proved that if a periodic group$\mathfrak{G}$ has an extremal normal divisor$\mathfrak{N}$, determining a complete abelian factor group$\mathfrak{G}/\mathfrak{N}$, then the center of the group$\mathfrak{G}$ contains a complete abelian subgroup$\mathfrak{A}$, satisfying the relation$\mathfrak{G} = \mathfrak{N}\mathfrak{A}$ and intersecting$\mathfrak{N}$ on a finite subgroup. It is also established with the aid of this proposition that every periodic group of automorphisms of an extremal group$\mathfrak{G}$ is a finite extension of a contained in it subgroup of inner automorphisms of the group$\mathfrak{G}$.