Electronic ISBN:  9781470410582 
Product Code:  MEMO/225/1058.E 
100 pp 
List Price:  $69.00 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 225; 2013MSC: 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 wellknown 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 wellknown 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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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 wellknown 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 wellknown 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