Abstract:
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 $\pi_1(\mathcal G)$ of a suitable finite graph ${\mathcal G}$ of groups. We prove a criterion for residuality by finite $\pi$-groups of tubular groups presented by trees of groups. Also we state a criterion for residuality by finite $p$-groups of tubular groups whose corresponding graph contains one edge outside a maximal subtree.
Keywords:residuality by $\pi$-groups, residual finiteness, tubular groups.
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