3-manifold groups are virtually residually p
- Matthias Aschenbrenner, Stefan Friedl.
- Providence, Rhode Island : American Mathematical Society, 
- Physical description
- vii, 100 pages : illustrations ; 26 cm.
- Memoirs of the American Mathematical Society ; no. 1058.
Science Library (Li and Ma)
|Shelved by Series title NO.1058||Unknown|
- Includes bibliographical references (pages 93-98) and index.
- Introduction Preliminaries Embedding theorems for $p$-Groups Residual properties of graphs of groups Proof of the main results The case of graph manifolds Bibliography Index.
- (source: Nielsen Book Data)9780821888018 20160612
- Publisher's Summary
- 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.
(source: Nielsen Book Data)9780821888018 20160612
- Publication date
- Title Variation
- Three-manifold groups are virtually residually p
- Memoirs of the American Mathematical Society, 0065-9266 ; number 1058
- "Volume 225, number 1058 (third of 4 numbers), September 2013."
- 9780821888018 (alk. paper)
- 0821888013 (alk. paper)
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