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Mat. Sb., 2019, Volume 210, Number 10, Pages 122–160 (Mi msb9115)  

Free products of groups are strongly verbally closed

A. M. Mazhuga

Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00591-а
This research was supported by the Russian Foundation for Basic Research (grant no. 19-01-00591-a).


DOI: https://doi.org/10.4213/sm9115

Full text: PDF file (945 kB)
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English version:
Sbornik: Mathematics, 2019, 210:10, 1456–1492

Bibliographic databases:

UDC: 512.543.7
MSC: Primary 20F70; Secondary 20E06, 20E08
Received: 01.04.2018

Citation: 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

Citation in format AMSBIB
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