A simple proof of a theorem of Karrass and Solitar

Delaram Kahrobaei

A simple proof of a theorem of Karrass and Solitar

Group Theory 2007-05-23 v1

Authors: Delaram Kahrobaei

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 $N\cap H = \{1\}$ .

Keywords

free groups finitely generated subgroups infinite index normal subgroup karrass-solitar theorem

Cite

@article{arxiv.math/0411076,
  title  = {A simple proof of a theorem of Karrass and Solitar},
  author = {Delaram Kahrobaei},
  journal= {arXiv preprint arXiv:math/0411076},
  year   = {2007}
}

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