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arXiv · 1010.2726

Virtual finite quotients of finitely generated groups

J. O. Button
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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.

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J. O. Button. 2010-10-13. Virtual finite quotients of finitely generated groups. https://arxiv.org/abs/1010.2726

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