3-manifold groups are virtually residually p
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Bibliographic Information
3-manifold groups are virtually residually p
（Memoirs of the American Mathematical Society, no. 1058）
American Mathematical Society, c2013
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Three-manifold groups are virtually residually p
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"September 2013, volume 225, number 1058 (third of 4 numbers)."
Includes bibliographical references (p. 93-98) and index
Description and Table of Contents
Description
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.
Table of Contents
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
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