Free products of groups are strongly verbally closed
A. M. Mazhuga
Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
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.
verbally closed subgroups, algebraically closed subgroups, retracts of groups.
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Sbornik: Mathematics, 2019, 210:10, 1456–1492
MSC: Primary 20F70; Secondary 20E06, 20E08
A. M. Mazhuga, “Free products of groups are strongly verbally closed”, Mat. Sb., 210:10 (2019), 122–160; Sb. Math., 210:10 (2019), 1456–1492
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\paper Free products of groups are strongly verbally closed
\jour Mat. Sb.
\jour Sb. Math.
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