3-Manifold Groups are Virtually Residually P (Memoirs of the American Mathematical Society 225, 1058)

3-Manifold Groups are Virtually Residually P (Memoirs of the American Mathematical Society 225, 1058)

By: Matthias Aschenbrenner (author), Stefan Friedl (author)Paperback

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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.

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About Author

Matthias Aschenbrenner , University of California, Los Angeles, CA, USA Stefan Friedl , University of Koln, Germany

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

Product Details

  • publication date: 30/09/2013
  • ISBN13: 9780821888018
  • Format: Paperback
  • Number Of Pages: 100
  • ID: 9780821888018
  • ISBN10: 0821888013

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