The Root Class Residuality of the Tree Product of Groups with Amalgamated Retracts
- Authors: Tumanova E.A.1
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Affiliations:
- Ivanovo State University
- Issue: Vol 60, No 4 (2019)
- Pages: 699-708
- Section: Article
- URL: https://journal-vniispk.ru/0037-4466/article/view/172551
- DOI: https://doi.org/10.1134/S0037446619040153
- ID: 172551
Cite item
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.
About the authors
E. A. Tumanova
Ivanovo State University
Author for correspondence.
Email: helenfog@bk.ru
Russian Federation, Ivanovo
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