xpyq = zr and groups that act freely on Λ-trees">

The equation xpyq = zr and groups that act freely on Λ-trees

• Brady, N. Department of Mathematics, University of Oklahoma, Norman, USA
• Ciobanu, Laura Department of Mathematics, University of Fribourg, Switzerland
• Martino, A. Department of Mathematics, Universitat Politecnica de Catalunya, Castelldefels, Spain
2009
Published in:
• Transactions of the American Mathematical Society. - 2009, vol. 361, no. 1, p. 223-236
English Let $G$ be a 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 $p$, $q$, $r\ge 4$, then $x$, $y$ and $z$ commute. As a result, the one-relator groups with ${x}^{p}{y}^{q}={z}^{r}$ as relator, are examples of hyperbolic and CAT($-1$) groups which do not act freely on any $\Lambda$-tree.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
• English
Classification
Mathematics