Abstract
Let [Formula: see text] be a nonempty class of finite groups closed under taking subgroups, quotients and extensions. We consider groups G endowed with their pro-[Formula: see text] topology, and say that G is 2-subgroup separable if whenever H and K are finitely generated closed subgroups of G, then the subset HK is closed. We prove that if the groups G1 and G2 are 2-subgroup separable, then so is their free product G1*G2. This extends a result to T. Coulbois. The proof uses actions of groups on abstract and profinite trees.
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