Abstract
Given a root class \( {\mathcal{C}} \) of groups, we establish some necessary and sufficient conditions for the \( {\mathcal{C}} \)-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 \( {\mathcal{C}} \)-residuality of some HNN-extensions and tree products.
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Funding
The study was supported by the Russian Science Foundation grant no. 22–21–00166, https://rscf.ru/en/ project/22-21-00166/.
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 2, pp. 405–422. https://doi.org/10.33048/smzh.2023.64.212
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Sokolov, E.V., Tumanova, E.A. The Root-Class Residuality of Some Generalized Free Products and HNN-Extensions. Sib Math J 64, 393–406 (2023). https://doi.org/10.1134/S003744662302012X
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DOI: https://doi.org/10.1134/S003744662302012X
Keywords
- root-class residuality of groups
- residual finiteness
- residual solvability
- generalized free product
- HNN-extension
- tree product