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On the Root-Class Residuality of Certain Free Products of Groups with Normal Amalgamated Subgroups

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Abstract

Let \({\cal K}\) be a root class of groups closed under taking quotient groups, G be a free product of groups A and B with amalgamated subgroups H and K. Let also H be normal in A, K be normal in B, and AutG(H) denote the set of automorphisms of H induced by all inner automorphisms of G. We prove a criterion for G to be residually a \({\cal K}\)-group provided AutG(H) is an abelian group or it satisfies some other conditions. We apply this result in the cases when A and B are bounded nilpotent groups or A/H, B/K ∈ \({\cal K}\).

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Funding

This work is supported by the Russian Foundation for Basic Research, project no. 18-31-00187.

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Authors and Affiliations

  1. Ivanovo State University, 39 Ermak str., Ivanovo, 153025, Russia

    E. V. Sokolov & E. A. Tumanova

Authors
  1. E. V. Sokolov
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  2. E. A. Tumanova
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Corresponding authors

Correspondence to E. V. Sokolov or E. A. Tumanova.

Additional information

Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 3, pp. 48–63.

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Sokolov, E.V., Tumanova, E.A. On the Root-Class Residuality of Certain Free Products of Groups with Normal Amalgamated Subgroups. Russ Math. 64, 43–56 (2020). https://doi.org/10.3103/S1066369X20030044

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  • DOI: https://doi.org/10.3103/S1066369X20030044

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