Effective coherence of groups discriminated by a locally quasi-convex hyperbolic group

2013/07/25 by Bumagin, Inna, Macdonald, Jeremy
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1307.6783

Abstract

We prove that every finitely generated group G discriminated by a locally quasi-convex torsion-free hyperbolic group Γ is effectively coherent: that is, presentations for finitely generated subgroups can be computed from the subgroup generators. We study G via its embedding into an iterated centralizer extension of Γ, and prove that this embedding can be computed. We also give algorithms to enumerate all finitely generated groups discriminated by Γ and to decide whether a given group, with decidable word problem, is discriminated by Γ. If Γ may have torsion, we prove that groups obtained from Γ by iterated amalgamated products with virtually abelian groups, over elementary subgroups, are effectively coherent.

Related

• Coherence, local quasiconvexity, and the perimeter of 2-complexes
• Finitely generated groups acting uniformly properly on hyperbolic space
• The generalised word problem for subgroups of hyperbolic groups
• Immutability is not uniformly decidable in hyperbolic groups
• One-relator groups with torsion are coherent