Vetenskap & teknik
Pocket
3-Manifold Groups Are Virtually Residually p
Matthias Aschenbrenner • Stefan Friedl
1269:-
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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 the authors prove a common generalisation 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.
- Format: Pocket/Paperback
- ISBN: 9780821888018
- Språk: Engelska
- Antal sidor: 100
- Utgivningsdatum: 2013-09-30
- Förlag: American Mathematical Society