Geodesic
Effective coherence of groups discriminated by a locally quasi-convex hyperbolic group
Inna Bumagin1 ; Jeremy Macdonald2
1Carleton University, Ottawa, Canada
2Stevens Institute of Technology, Hoboken, USA
Groups, geometry, and dynamics, Tome 10 (2016) no. 2, pp. 545-582

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DOI

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.
DOI : 10.4171/ggd/356
Classification : 20-XX
Mots-clés : Hyperbolic groups, quasi-convexity, discrimination, subgroup presentations, algorithms

Inna Bumagin  1   ; Jeremy Macdonald  2

1 Carleton University, Ottawa, Canada
2 Stevens Institute of Technology, Hoboken, USA 
Inna Bumagin; Jeremy Macdonald. Effective coherence of groups discriminated by a locally quasi-convex hyperbolic group. Groups, geometry, and dynamics, Tome 10 (2016) no. 2, pp. 545-582. doi: 10.4171/ggd/356
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     year = {2016},
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