Virtual finite quotients of finitely generated groups

zbMATH Open1237.20024arXiv1010.2726MaRDI QIDQ3091721

Jack Button

Publication date: 12 September 2011

Abstract: If G is a semidirect product N by H with N normal and finitely generated then G has the property that every finite group is a quotient of some finite index subgroup of G if and only if one of N and H has this property. This has applications to 3-manifolds and to cyclically presented groups, for instance for any fibred hyperbolic 3-manifold M and any finite simple group S, there is a cyclic cover of M whose fundamental group surjects to S. We also give a short proof of the residual finiteness of ascending HNN extensions of finite rank free groups when the induced map on homology is injective.

Full work available at URL: https://arxiv.org/abs/1010.2726

zbMATH Keywords

subgroups of finite indexfinitely generated groupsfinite quotient groupsvirtual quotients

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Residual properties and generalizations; residually finite groups (20E26)

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