# On the intersection of free subgroups in free products of groups

@article{Dicks2008OnTI, title={On the intersection of free subgroups in free products of groups}, author={Warren Dicks and S. Ivanov}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, year={2008}, volume={144}, pages={511 - 534} }

Abstract Let (Gi | i ∈ I) be a family of groups, let F be a free group, and let $G = F \ast \mathop{\text{\Large $*$}}_{i\in I} G_i,$ the free product of F and all the Gi. Let $\mathcal{F}$ denote the set of all finitely generated subgroups H of G which have the property that, for each g ∈ G and each i ∈ I, $H \cap G_i^{g} = \{1\}.$ By the Kurosh Subgroup Theorem, every element of $\mathcal{F}$ is a free group. For each free group H, the reduced rank of H, denoted r(H), is defined as $\max… Expand

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