The equation x^py^q=z^r and groups that act freely on \Lambda-trees
The equation x^py^q=z^r and groups that act freely on \Lambda-trees
Let $G$ be a finitely generated group that acts freely on a $\Lambda$-tree, where $\Lambda$ is an ordered abelian group, and let $x, y, z$ be elements in $G$. We show that if $x^p y^q = z^r$ with integers $p$, $q$, $r \geq 4$, then $x$, $y$ and $z$ commute.
223-236
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Brady, Noel
466bfef1-bc8f-4086-95cf-927148f3ab68
Ciobanu, Laura
67910c7a-0938-4111-a53e-987d9ca6549a
O Rourke, Shane
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1 January 2009
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Brady, Noel
466bfef1-bc8f-4086-95cf-927148f3ab68
Ciobanu, Laura
67910c7a-0938-4111-a53e-987d9ca6549a
O Rourke, Shane
c3e01ffa-2948-4c1a-8e88-98e8650edd55
Martino, Armando, Brady, Noel, Ciobanu, Laura and O Rourke, Shane
(2009)
The equation x^py^q=z^r and groups that act freely on \Lambda-trees.
Transactions of the American Mathematical Society, 361 (1), .
(doi:10.1090/S0002-9947-08-04639-4).
Abstract
Let $G$ be a finitely generated group that acts freely on a $\Lambda$-tree, where $\Lambda$ is an ordered abelian group, and let $x, y, z$ be elements in $G$. We show that if $x^p y^q = z^r$ with integers $p$, $q$, $r \geq 4$, then $x$, $y$ and $z$ commute.
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lyndon_and_lambda.pdf
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Published date: 1 January 2009
Organisations:
Mathematics
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Local EPrints ID: 155687
URI: http://eprints.soton.ac.uk/id/eprint/155687
ISSN: 0002-9947
PURE UUID: c5503794-1119-4bce-9e73-ff3a0ce8e9e6
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Date deposited: 28 May 2010 12:08
Last modified: 14 Mar 2024 02:54
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Author:
Noel Brady
Author:
Laura Ciobanu
Author:
Shane O Rourke
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