This article is cited in 11 papers

Verbally closed virtually free subgroups

Ant. A. Klyachko, A. M. Mazhuga

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A theorem of Myasnikov and Roman'kov says that any verbally closed subgroup of a finitely generated free group is a retract. We prove that all free (and many virtually free) verbally closed subgroups are retracts in any finitely generated group.
Bibliography: 14 titles.

Keywords: verbally closed subgroups, algebraically closed subgroups, retracts.

UDC: 512.543.7

MSC: Primary 20F70; Secondary 20E05, 20E08

Received: 13.03.2017 and 04.07.2017

DOI: 10.4213/sm8942

 English version: Sbornik: Mathematics, 2018, 209:6, 850–856

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