Verbal subgroups of complete direct products of groups

S. A. Ashmanov

M. V. Lomonosov Moscow State University

Abstract: It is proved that if $V(X)$ is a proper verbal subgroup of a free group $X$ of countable rank, then a verbal subgroup $V(H)$ of the complete direct product $H=\widetilde\Pi^\times X_i$ of a countable number of isomorphic copies $X_i$ of $X$ differs from the complete direct product $\widetilde\Pi^\times V(X_i)$.

UDC: 512.4

Received: 20.01.1970

 English version: Mathematical Notes, 1971, 9:6, 399–401

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