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Sbornik: Mathematics, 2019, Volume 210, Issue 10, Pages 1456–1492
DOI: https://doi.org/10.1070/SM9115 (Mi sm9115) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Free products of groups are strongly verbally closed

A. M. Mazhuga

Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
English version PDF (769 kB) Citations (4) Russian version article
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DOI: https://doi.org/10.1070/SM9115
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).
Received: 01.04.2018
Bibliographic databases:
Document Type: Article
UDC: 512.543.7
MSC: Primary 20F70; Secondary 20E06, 20E08
Language: English
Original paper language: Russian
Citation: A. M. Mazhuga, “Free products of groups are strongly verbally closed”, Sb. Math., 210:10 (2019), 1456–1492
Citation in format AMSBIB
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\by A.~M.~Mazhuga
\paper Free products of groups are strongly verbally closed
\jour Sb. Math.
\yr 2019
\vol 210
\issue 10
\pages 1456--1492
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  • https://doi.org/10.1070/SM9115
  • https://www.mathnet.ru/eng/sm/v210/i10/p122
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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