Abstract:
In a number of recent papers it was established that many almost free groups, fundamental groups of almost all connected surfaces, and all groups that are nontrivial free products of groups with identities are algebraically closed in any group in which they are verbally closed. In the present paper we establish that any group that is a nontrivial free product of groups is algebraically closed in any group in which it is verbally closed.
Bibliography: 13 titles.
Keywords:verbally closed subgroups, algebraically closed subgroups, retracts of groups.
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