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Residual properties of 3-manifold groups
Let p be a prime. A group is called residually p if for any non-trivial element there exists a homomorphism to a p-group such that the image of the element is non-trivial. A group is called virtually residually p, if it contains a finite index which is residually p. It is well-known that linear groups are virtually residually p. Hyperbolic 3-manifolds have linear fundamental groups and it is an open problem whether all 3-manifold groups are linear. We will show that any 3-manifold group is virtually residually p. This is joint work with Matthias Aschenbrenner.
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