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 Mat. Zametki, 2019, Volume 105, Issue 1, Pages 65–75 (Mi mz11726)

On a Family of Residually Finite Groups

D. I. Moldavanskii

Ivanovo State University

Abstract: As is known, there is a finitely generated residually finite group (for short, a residually $\mathcal F$-group) whose extension by some finite group is not a residually $\mathcal F$-group. In the paper, it is shown that, nevertheless, every extension of a finite group by a finitely generated residually $\mathcal F$-group is a Hopf group, and every extension of a center-free finite group by a finitely generated residually $\mathcal F$-group is a residually $\mathcal F$-group. If a finitely generated residually $\mathcal F$-group $G$ is such that every extension of an arbitrary finite group by $G$ is a residually $\mathcal F$-group, then a descending HNN-extension of the group $G$ also has the same property, provided that it is a residually $\mathcal F$-group.

Keywords: residually finite groups, HNN-extensions of groups.

DOI: https://doi.org/10.4213/mzm11726

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Document Type: Article
UDC: 512.543

Citation: D. I. Moldavanskii, “On a Family of Residually Finite Groups”, Mat. Zametki, 105:1 (2019), 65–75

Citation in format AMSBIB
\Bibitem{Mol19} \by D.~I.~Moldavanskii \paper On a Family of Residually Finite Groups \jour Mat. Zametki \yr 2019 \vol 105 \issue 1 \pages 65--75 \mathnet{http://mi.mathnet.ru/mz11726} \crossref{https://doi.org/10.4213/mzm11726} \elib{http://elibrary.ru/item.asp?id=36603825}