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On periodic groups of automorphisms of extremal groups

Authors:	S N Chernikov

Institution:	(1) Mathematical Institute of the Academy of Sciences of the Ukrainian SSR, USSR

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 $\mathfrak{G}$ .Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 91–96, July, 1968.

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