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

Сибирский математический журнал

article

E. A. Tumanova¹ 

[1] Ivanovo State University

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

DOI  :  10.1134/S0037446619040153

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY