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Lookup NU author(s): Professor Sarah Rees
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).
We prove that, for a finitely generated group hyperbolic relative to virtually abelian subgroups, the generalised word problem for a parabolic subgroup is the language of a rela-time Turing machine. Then, for a hyperbolic group, we show that the generalised word problem for a quasiconvex subgroup is a real-time language under either of two additional hypotheses on the subgroup.By extending the Muller-Schupp theorem we show that the generalised word problem for a finitely generated subgroup of a finitely generated virtually free group is context-free. Conversely, we prove 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.
Author(s): Ciobanu L, Holt D, Rees s
Publication type: Article
Publication status: Published
Journal: Journal of Algebra
Print publication date: 15/12/2018
Online publication date: 17/09/2018
Acceptance date: 23/09/2018
Date deposited: 06/11/2018
ISSN (print): 0021-8693
ISSN (electronic): 1090-266X
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