The equation <span class=

The equation x^py^q = z^r 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
Rourke, S. O. Department of Mathematics, Cork Institute of Technology, Ireland

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

Λ

-tree, where

Λ

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. 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

Λ

-tree.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language

Classification

Mathematics

License

License undefined

Identifiers

Persistent URL

https://folia.unifr.ch/unifr/documents/300874

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