This article is cited in 3 papers

FC groups whose periodic parts can be embedded in direct products of finite groups

L. A. Kurdachenko

Dnepropetrovsk State University

Abstract: In this note are considered $FC$ groups whose periodic parts can be embedded in direct products of finite groups. It is shown that if the periodic part of an $FC$ group $G$ can be embedded in the direct product of its finite factor groups with respect to the normal subgroups of $G$ whose intersection is the trivial subgroup, then $G/Z(G)$ is a subgroup of a direct product of finite groups. It is also shown that if the periodic part of an $FC$ group $G$ is a group without a center, then $G$ can be embedded in a direct product of finite groups without centers and a torsion-free Abelian group.

UDC: 519

Received: 21.04.1975

 English version: Mathematical Notes, 1977, 21:1, 6–12

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