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.