The generalised word problem for subgroups of hyperbolic groups
arXiv:1505.02397
Abstract
We prove that the generalised word problem of a finitely generated subgroup of a finitely generated virtually free group is context-free, that a hyperbolic group must be virtually free if it has a torsion-free quasiconvex subgroup of infinite index with context-free generalised word problem, and that, for any hyperbolic group, the generalised word problem of a torsion-free quasiconvex subgroup is recognised by a real-time Turing machine.
This article is withdrawn because it is now included as a part of the article `The generalised word problem in hyperbolic and relatively hyperbolic groups' (Laura Ciobanu, Derek Holt and Sarah Rees),on arXiv since 3rd Nov 2015 as arXiv:1511.00548 Please update citations accordingly