On a conjecture of Karrass and Solitar

Abstract

We settle an old conjecture of Karrass and Solitar by proving that a finitely generated subgroup of a non-trivial free product $G = A\ast B$ has finite index if and only if it intersects non-trivially each non-trivial normal subgroup of $G$. This holds, more generally, for subgroups of finite Kurosh rank.