We construct an example of a torsion free freely indecomposablefinitely presented non-quasiconvex subgroup H of a word hyperbolicgroup G such that the limit set of H is not the limit set of aquasiconvex subgroup of G. In particular, this gives acounterexample to the conjecture of G. Swarup that a finitely presentedone-ended subgroup of a word hyperbolic group is quasiconvex if andonly if it has finite index in its virtual normalizer.
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