This article is cited in 6 papers

On periodic groups of automorphisms of extremal groups

S. N. Chernikov

Mathematics Institute, Academy of Sciences of the Ukrainian SSR

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 $\mathfrak G=\mathfrak{NA}$ 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 $\mathfrak G$.

UDC: 512.4

Received: 29.02.1968

 English version: Mathematical Notes, 1968, 4:1, 543–545

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