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The equation x^py^q=z^r and groups that act freely on \Lambda-trees

By Armando Martino, Noel Brady, Laura Ciobanu and Shane O Rourke


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

Year: 2009
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Provided by: e-Prints Soton
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    1. (1997). An algorithm for cellular maps of closed surfaces.
    2. (2006). Cubulating graphs of free groups with cyclic edge groups. In preparation, doi
    3. (2001). Diophantine geometry over groups. I. Makanin-Razborov diagrams. doi
    4. (2005). Free actions on Zn-trees: A survey. doi
    5. (1989). free groups. doi
    6. (1994). Generalizations of free groups: Some questions. doi
    7. (1991). Group actions on non-Archimedean trees. In Arboreal group theory (Berkeley, CA, 1988),v o l u m e1 9o fM a t h .S c i .R e s .I n s t .P u b l . doi
    8. (2001). Introduction to Λ-trees. World Scientific, doi
    9. (1998). Irreducible affine varieties over a free group I. Irreducibility of quadratic equations and Nullstellensatz. doi
    10. (2004). Limit groups and groups acting freely on Rn-trees. doi
    11. (1960). On a problem of Lyndon. doi
    12. (1962). On generalised free products. doi
    13. (1967). Residually free groups. doi
    14. (1962). Sch¨ utzenberger. The equation aM = bNcP in a free group.
    15. (1990). Small cancellation theory and automatic groups. doi
    16. (1995). Some examples of groups with no nontrivial action on a Λ-tree. doi
    17. (2004). Some free actions on non-Archimedean trees. doi
    18. (1959). Sur l’´ equation a2+n = b2+mc2+p dans un groupe libre.
    19. (1959). The equation a2b2 = c2 in free groups.
    20. (1959). The equation anbn = cn in a free group. doi

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