Residual π-Finiteness of Tubular Groups

A finitely generated group G, which acts on a tree so that all edge stabilizers are infinite cyclic groups and all vertex stabilizers are free rank 2 Abelian groups, is called a tubular group. Every tubular group is isomorphic to the fundamental group π₁(𝒢) of a suitable finite graph 𝒢 of groups. We prove a criterion for residual π-finiteness of tubular groups presented by trees of groups. Also we state a criterion for residual p-finiteness of tubular groups whose corresponding graph contains one edge outside a maximal subtree.