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Rank and Nielsen equivalence in hyperbolic extensions. (English) Zbl 1515.20239

Summary: In this note, we generalize a theorem of J. Souto [Geom. Topol. Monogr. 14, 505–518 (2008; Zbl 1144.57017)] on rank and Nielsen equivalence in the fundamental group of a hyperbolic fibered \(3\)-manifold to a large class of hyperbolic group extensions. This includes all hyperbolic extensions of surfaces groups as well as hyperbolic extensions of free groups by convex cocompact subgroups of \(\mathrm{Out}(F_n)\).

MSC:

20F67 Hyperbolic groups and nonpositively curved groups
20E22 Extensions, wreath products, and other compositions of groups
20F65 Geometric group theory
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
57M07 Topological methods in group theory

Citations:

Zbl 1144.57017
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References:

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