The generalised word problem for subgroups of hyperbolic groups

2015/05/10 by Derek F. Holt, Sarah Rees, Holt, Derek F. +1
Mathematics · Computer Science · #Geometric and Algebraic Topology #semigroups and automata theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/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.

Related

• The generalised word problem in hyperbolic and relatively hyperbolic groups
• A note on Context Sensitive languages and Word Problems
• The compressed word problem in relatively hyperbolic groups
• Hyperbolic groups and free constructions
• Exponentially generic subsets of groups