This article is cited in 7 papers

The root-class residuality of tree products with central amalgamated subgroups

E. V. Sokolov, E. A. Tumanova

Ivanovo State University

Abstract: Given a root class ${\Cal C}$ 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 ${\Cal C}$-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.

Keywords: tree product, residual finiteness, residual $p$-finiteness, residual solvability, root-class residuality.

UDC: 512.543

MSC: 20E26, 20E06

Received: 06.11.2019
Revised: 26.02.2020
Accepted: 08.04.2020

DOI: 10.33048/smzh.2020.61.318

 English version: Siberian Mathematical Journal, 2020, 61:3, 545–551

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