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Preprint Number 244
244. Matthias Aschenbrenner, Stefan Friedl
3-manifold groups are virtually residually p
Submission date: 29 April 2010.
Given a prime p, a group is called residually p if the intersection of its p-power index normal subgroups is trivial. A group is called virtually residually p if it has a finite index subgroup which is residually p. It is well-known that finitely generated linear groups over fields of characteristic zero are virtually residually p for all but finitely many p. In particular, fundamental groups of hyperbolic 3-manifolds are virtually residually p. It is also well-known that fundamental groups of 3-manifolds are residually finite. In this paper we prove a common generalization of these results: every 3-manifold group is virtually residually p for all but finitely many p. This gives evidence for the conjecture (Thurston) that fundamental groups of 3-manifolds are linear groups.
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