3-manifold groups are virtually residually p /
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| Author / Creator: | Aschenbrenner, Matthias, 1972- author. |
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| Imprint: | Providence, Rhode Island : American Mathematical Society, [2013] |
| Description: | vii, 100 pages : illustrations ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 0065-9266 ; number 1058 Memoirs of the American Mathematical Society ; no. 1058. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/9793909 |
| Summary: | 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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| Item Description: | "Volume 225, number 1058 (third of 4 numbers), September 2013." |
| Physical Description: | vii, 100 pages : illustrations ; 26 cm. |
| Bibliography: | Includes bibliographical references (pages 93-98) and index. |
| ISBN: | 9780821888018 0821888013 |
| ISSN: | 0065-9266 ; |
