On the intersection of tame subgroups in groups acting on trees

Abstract

Let [Formula: see text] be a group acting on a tree [Formula: see text] with finite edge stabilizers of bounded order. We provide, in some very interesting cases, upper bounds for the complexity of the intersection [Formula: see text] of two tame subgroups [Formula: see text] and [Formula: see text] of [Formula: see text] in terms of the complexities of [Formula: see text] and [Formula: see text]. In particular, we obtain bounds for the Kurosh rank [Formula: see text] of the intersection in terms of Kurosh ranks [Formula: see text] and [Formula: see text], in the case, where [Formula: see text] and [Formula: see text] act freely on the edges of [Formula: see text].