Abstract:
Given a root class CC of groups, we establish some necessary and sufficient conditions for the C-residuality of the free product of the two groups with amalgamated subgroups one of which is central in the corresponding free factor. We apply these results to obtain the criteria and sufficient conditions for the C-residuality of some HNN-extensions and tree products.
Keywords:
root-class residuality of groups, residual finiteness, residual solvability, generalized free product, HNN-extension, tree product.
Citation:
E. V. Sokolov, E. A. Tumanova, “The root-class residuality of some generalized free products and HNN-extensions”, Sibirsk. Mat. Zh., 64:2 (2023), 405–422; Siberian Math. J., 64:2 (2023), 393–406
\Bibitem{SokTum23}
\by E.~V.~Sokolov, E.~A.~Tumanova
\paper The root-class residuality of some generalized free products and HNN-extensions
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 2
\pages 405--422
\mathnet{http://mi.mathnet.ru/smj7769}
\crossref{https://doi.org/10.33048/smzh.2023.64.212}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 2
\pages 393--406
\crossref{https://doi.org/10.1134/S003744662302012X}
Linking options:
https://www.mathnet.ru/eng/smj7769
https://www.mathnet.ru/eng/smj/v64/i2/p405
This publication is cited in the following 4 articles:
E. V. Sokolov, “On the Separability of Abelian Subgroups of the Fundamental Groups of Graphs of Groups. II”, Sib Math J, 65:1 (2024), 174
E. V. Sokolov, “Ob otdelimosti abelevykh podgrupp fundamentalnykh grupp grafov grupp. II”, Sib. matem. zhurn., 65:1 (2024), 207–228
E.V. Sokolov, “On the residual nilpotence of generalized free products of groups”, Journal of Algebra, 657 (2024), 292
E. V. Sokolov, “On Conditions for the Approximability of the Fundamental Groups of Graphs of Groups by Root Classes of Groups”, Lobachevskii J Math, 44:12 (2023), 5444
Citation in format AMSBIB
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