S. O'Rourke

will speak on

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

Time: 12:00PM
Date: Mon 3rd September 2007
Location: ENG226 [map]

Further information

Abstract: It is a classical result due to Lyndon and Schützenberger that in a free group,
solutions of the equation class="cmmi-12">x^{class="cmmi-8">p}class="cmmi-12">y^{class="cmmi-8">q} = class="cmmi-12">z^{class="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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