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Siberian Mathematical Journal

, Volume 60, Issue 4, pp 699–708 | Cite as

The Root Class Residuality of the Tree Product of Groups with Amalgamated Retracts

  • E. A. TumanovaEmail author
Article

Abstract

Given a root class \(\mathscr{K}\) of groups, we prove that the tree product of residually \(\mathscr{K}\)-groups with amalgamated retracts is a residually \(\mathscr{K}\)-group. This yields a criterion for the \(\mathscr{K}\)-residuality of Artin and Coxeter groups with tree structure. We also prove that the HNN-extension X of a residually \(\mathscr{K}\)-group B is a residually \(\mathscr{K}\)-group provided that the associated subgroups of X are retracts in B and \(\mathscr{K}\) contains at least one nonperiodic group.

Keywords

tree product of groups HNN-extension Artin group Coxeter group root class residuality residual finiteness residual p-finiteness residual solubility 

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Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Ivanovo State UniversityIvanovoRussia

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