The Root-Class Residuality of Tree Products with Central Amalgamated Subgroups

Abstract

Given a root class \(\mathscr{C}\) of groups and a tree product P in which each amalgamated subgroup lies in the centers of the corresponding vertex groups, we point out certain sufficient conditions for the \(\mathscr{C}\)-residuality of P. In particular, we show that the tree product of solvable groups of bounded derived length with central amalgamated subgroups is residually solvable.

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

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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 692–702.

The authors were partially supported by the Russian Foundation for Basic Research (Grant 18-31-00187).

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Sokolov, E.V., Tumanova, E.A. The Root-Class Residuality of Tree Products with Central Amalgamated Subgroups. Sib Math J 61, 545–551 (2020). https://doi.org/10.1134/S0037446620030180

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Keywords

  • tree product
  • residual finiteness
  • residual p-finiteness
  • residual solvability
  • root-class residuality