A simple proof of a theorem of Karrass and Solitar

Abstract

In this note we give a particularly short and simple proof of the following theorem of Karrass and Solitar. Let $H$ be a finitely generated subgroup of a free group $F$ with infinite index $[F:H]$. Then there is a nontrivial normal subgroup $N$ of $F$ such that $N\cap H=\{1\}$.

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