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

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Keywords Algorithms., Discrimination, Hyperbolic groups, Quasi-convexity, Subgroup presentations
Persistent URL dx.doi.org/10.4171/GGD/356
Journal Groups, Geometry, and Dynamics
Bumagin, I, & Macdonald, J. (Jeremy). (2016). Effective coherence of groups discriminated by a locally quasi-convex hyperbolic group. Groups, Geometry, and Dynamics, 10(2), 545–582. doi:10.4171/GGD/356