The equation x^{p}y^{q}=z^{r} in tree-free groups

**Speaker**: S. O'Rourke

**Time**: 12:00PM**Date**: Mon 3rd September 2007

**Location**: ENG226

**Abstract**

It is a classical result due to Lyndon and Schützenberger that in a free group, solutions of the equation class="cmmi-12">xclass="cmmi-8">pclass="cmmi-12">yclass="cmmi-8">q = class="cmmi-12">zclass="cmmi-8">r commute for integers class="cmmi-12">p,q,r class="cmsy-10x-x-120">≥ 2. Groups that admit a free action (without inversions) on a Λ-tree for some ordered abelian group Λ — so-called class="cmti-12">tree-free groups — are a natural generalisation of free groups, and they satisfy many of the same properties as free groups. On the other hand this class properly contains fully residually free groups (called limit groups by Sela).

In this talk we will discuss the extent to which the result of Lyndon and Schützenberger extends to tree-free groups.

This is joint work with N. Brady, L. Ciobanu and A. Martino.

It is a classical result due to Lyndon and Schützenberger extends to tree-free groups.

This is joint work with N. Brady, L. Ciobanu and A. Martino.

(This talk is part of the IMS September Meeting 2007 series.)

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