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Item Details
| Title:
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3-MANIFOLD GROUPS ARE VIRTUALLY RESIDUALLY P
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| By: |
Matthias Aschenbrenner, Stefan Friedl |
| Format: |
Paperback |
| List price:
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£65.00 |
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We believe that this item is permanently unavailable, and so we cannot source
it.
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| ISBN 10: |
0821888013 |
| ISBN 13: |
9780821888018 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
30 September, 2013 |
| Series: |
Memoirs of the American Mathematical Society 225, 1058 |
| Pages: |
100 |
| 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 . This gives evidence for the conjecture (Thurston) that fundamental groups of $3$-manifolds are linear groups. |
| Synopsis: |
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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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