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

We prove that every finitely generated group G discriminated by a locally quasi-convex torsion-free hyperbolic group Gamma 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 Gamma, and prove that this embedding can be computed. We also give algorithms to enumerate all finitely generated groups discriminated by Gamma and to decide whether a given group, with decidable word problem, is discriminated by Gamma. If Gamma may have torsion, we prove that groups obtained from Gamma by iterated amalgamated products with virtually abelian groups, over elementary subgroups, are effectively coherent.