The generalised word problem for subgroups of hyperbolic groups

Derek F. Holt; Sarah Rees

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arXiv · 1505.02397

The generalised word problem for subgroups of hyperbolic groups

Derek F. Holt·Sarah Rees

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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.

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Derek F. Holt, Sarah Rees. 2015-11-03. The generalised word problem for subgroups of hyperbolic groups. https://arxiv.org/abs/1505.02397

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