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 Mat. Zametki, 2015, Volume 97, Issue 5, Pages 767–780 (Mi mz10396)

On the Conjugacy Separability of Some Free Constructions of Groups by Root Classes of Finite Groups

E. V. Sokolov

Ivanovo State University

Abstract: Let $\mathcal{C}$ be an arbitrary class of groups which has the root property, consists of finite groups only, and contains at least one nonidentity group. It is proved that every extension of a free group by a $\mathcal{C}$-group is conjugacy $\mathcal{C}$-separable. It is also proved that, if $G$ is a free product of two conjugacy $\mathcal{C}$-separable groups with finite amalgamated subgroup or an HNN-extension of a conjugacy $\mathcal{C}$-separable group with finite associated subgroups, then the group $G$ is residually $\mathcal{C}$ if and only if it is conjugacy $\mathcal{C}$-separable.

Keywords: class of groups which has the root property, HNN-extension, free product with finite amalgamated subgroup, residually $\mathcal{C}$ group, conjugacy $\mathcal{C}$-separable group.

DOI: https://doi.org/10.4213/mzm10396

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English version:
Mathematical Notes, 2015, 97:5, 779–790

Bibliographic databases:

Document Type: Article
UDC: 512.543

Citation: E. V. Sokolov, “On the Conjugacy Separability of Some Free Constructions of Groups by Root Classes of Finite Groups”, Mat. Zametki, 97:5 (2015), 767–780; Math. Notes, 97:5 (2015), 779–790

Citation in format AMSBIB
\Bibitem{Sok15} \by E.~V.~Sokolov \paper On the Conjugacy Separability of Some Free Constructions of Groups by Root Classes of Finite Groups \jour Mat. Zametki \yr 2015 \vol 97 \issue 5 \pages 767--780 \mathnet{http://mi.mathnet.ru/mz10396} \crossref{https://doi.org/10.4213/mzm10396} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3370560} \elib{http://elibrary.ru/item.asp?id=23421563} \transl \jour Math. Notes \yr 2015 \vol 97 \issue 5 \pages 779--790 \crossref{https://doi.org/10.1134/S0001434615050132} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000357050200013} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84933526971} 

• http://mi.mathnet.ru/eng/mz10396
• https://doi.org/10.4213/mzm10396
• http://mi.mathnet.ru/eng/mz/v97/i5/p767

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This publication is cited in the following articles:
1. E. A. Tumanova, “On the root-class residuality of generalized free products with a normal amalgamation”, Russian Math. (Iz. VUZ), 59:10 (2015), 23–37
2. E. V. Sokolov, E. A. Tumanova, “Sufficient conditions for the root-class residuality of certain generalized free products”, Siberian Math. J., 57:1 (2016), 135–144
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