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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
Front Cover for 3-Manifold Groups Are Virtually Residually $p$
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
Front Cover for 3-Manifold Groups Are Virtually Residually $p$
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  • Front Cover for 3-Manifold Groups Are Virtually Residually $p$
  • Back Cover for 3-Manifold Groups Are Virtually Residually $p$
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.

  • Table of Contents
     
     
    • 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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