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3-Manifold Groups Are Virtually Residually $p$

Matthias Aschenbrenner University of California, Los Angeles, Los Angeles, CA
Stefan Friedl University of Koln, Koln, Germany
Available Formats:
Electronic ISBN: 978-1-4704-1058-2
Product Code: MEMO/225/1058.E
100 pp
List Price: $69.00 MAA Member Price:$62.10
AMS Member Price: $41.40 Click above image for expanded view 3-Manifold Groups Are Virtually Residually$p$Matthias Aschenbrenner University of California, Los Angeles, Los Angeles, CA Stefan Friedl University of Koln, Koln, Germany Available Formats:  Electronic ISBN: 978-1-4704-1058-2 Product Code: MEMO/225/1058.E 100 pp  List Price:$69.00 MAA Member Price: $62.10 AMS Member Price:$41.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 2252013
MSC: Primary 20; 57;

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 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.

• Chapters
• Introduction
• 1. Preliminaries
• 2. Embedding Theorems for $p$-Groups
• 3. Residual Properties of Graphs of Groups
• 4. Proof of the Main Results
• 5. The Case of Graph Manifolds
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Volume: 2252013
MSC: Primary 20; 57;

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 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.

• Chapters
• Introduction
• 1. Preliminaries
• 2. Embedding Theorems for $p$-Groups
• 3. Residual Properties of Graphs of Groups
• 4. Proof of the Main Results
• 5. The Case of Graph Manifolds
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