Virtual finite quotients of finitely generated groups
Group Theory
2010-10-14 v1
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.
Keywords
Cite
@article{arxiv.1010.2726,
title = {Virtual finite quotients of finitely generated groups},
author = {J. O. Button},
journal= {arXiv preprint arXiv:1010.2726},
year = {2010}
}