E. A. Tumanova, “On the root-class residuality of generalized free products with a normal amalgamation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 10, 27–44; Russian Math. (Iz. VUZ), 59:10 (2015), 23

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 10, Pages 27–44 (Mi ivm9041)

This article is cited in 20 scientific papers (total in 20 papers)

On the root-class residuality of generalized free products with a normal amalgamation

E. A. Tumanova^ab

^a Chair of the Higher Mathematics and Information Science, Ivanovo Fire and Rescue Academy, 33 Stroitelei Ave., Ivanovo, 153040 Russia
^b Chair of Algebra and Mathematical Logic, Ivanovo State University, 39 Ermaka str., Ivanovo, 153025 Russia

Full-text PDF (265 kB) Citations (20)

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Abstract: We obtain both necessary and sufficient conditions for the free product of two groups with normal amalgamated subgroups to be a residually

$\mathcal C$ -group, where

$\mathcal C$ is a root class of groups, which must be homomorphically closed in most cases.

Keywords: generalized free product, residual property, root class of groups.

Received: 23.02.2014

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 10, Pages 23–37
DOI: https://doi.org/10.3103/S1066369X15100035

Bibliographic databases:

Document Type: Article

UDC: 512.543

Language: Russian

Citation: E. A. Tumanova, “On the root-class residuality of generalized free products with a normal amalgamation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 10, 27–44; Russian Math. (Iz. VUZ), 59:10 (2015), 23–37

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/ivm9041

https://www.mathnet.ru/eng/ivm/y2015/i10/p27

This publication is cited in the following 20 articles:

D. R. Baranov, E. V. Sokolov, “On the Separability of Abelian Subgroups of the Generalized Free Product of Two Groups with Normal Amalgamated Subgroup”, Sib Math J, 66:2 (2025), 262
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, E. A. Tumanova, “The root-class residuality of some generalized free products and HNN-extensions”, Siberian Math. J., 64:2 (2023), 393–406
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
E. V. Sokolov, “The root-class residuality of the fundamental groups of graphs of groups”, Siberian Math. J., 62:4 (2021), 719–729
E. V. Sokolov, E. A. Tumanova, “On the root-class residuality of certain free products of groups with normal amalgamated subgroups”, Russian Math. (Iz. VUZ), 64:3 (2020), 43–56
E. V. Sokolov, E. A. Tumanova, “The root-class residuality of tree products with central amalgamated subgroups”, Siberian Math. J., 61:3 (2020), 545–551
E. A. Tumanova, “On the root-class residuality of certain HNN-extensions of groups”, Russian Math. (Iz. VUZ), 64:12 (2020), 38–45
E. A. Tumanova, “On the residual properties of generalized direct products of groups”, Lobachevskii J. Math., 41:9, SI (2020), 1704–1711
E. V. Sokolov, E. A. Tumanova, “To the question of the root-class residuality of free constructions of groups”, Lobachevskii J. Math., 41:2, SI (2020), 260–272
E. A. Tumanova, “The root class residuality of the tree product of groups with amalgamated retracts”, Siberian Math. J., 60:4 (2019), 699–708
E. V. Sokolov, E. A. Tumanova, “Generalized direct products of groups and their application to the study of residuality of free constructions of groups”, Algebra and Logic, 58:6 (2020), 480–493
A. E. Kuvaev, E. V. Sokolov, “Necessary conditions of the approximability of generalized free products and HNN-extensions”, Russian Math. (Iz. VUZ), 61:9 (2017), 32–42
E. V. Sokolov, E. A. Tumanova, “Root Class Residuality of HNN-Extensions with Central Cyclic Associated Subgroups”, Math. Notes, 102:4 (2017), 556–568
E. V. Sokolov, “Separability of the subgroups of residually nilpotent groups in the class of finite $\pi$-groups”, Siberian Math. J., 58:1 (2017), 169–175
E. A. Tumanova, “The root class residuality of Baumslag–Solitar groups”, Siberian Math. J., 58:3 (2017), 546–552
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
A. V. Rozov, E. V. Sokolov, “O nilpotentnoi approksimiruemosti svobodnykh proizvedenii nilpotentnykh grupp s tsentralnymi ob'edinennymi podgruppami”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 6(44), 34–44

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