The generalised word problem for subgroups of hyperbolic groups

Derek F. Holt and Sarah Rees

Keywords

generalised word problem, hyperbolic groups, context-free language, real-time Turing machine

Status

Published in J. Algebra 516 (2018) 149--171.

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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