**Financial support through the following projects:**

UIDB/00297/2020

UID/MAT/00297/2019

UID/MAT/00297/2013

PEst-OE/MAT/UI0297/2014

PEst-OE/MAT/UI0297/2011

Monday, 22 June 2015, 2:00 p.m.

Lecturer: Prof.ª Dr.ª Tara Brough (Research Fellow in Algebra, School of Mathematics and Statistics, Mathematical Institute St Andrews, SCOTLAND)

Title: "Detecting solubility for finitely generated groups of piecewise-linear homeomorphisms"

Local: Room 1.4, Edifício VII

Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: The group PL_o(I) consists of all orientation-preserving piecewise-linear homeomorphisms of the unit interval. The finitely generated subgroups of PL_o(I) include many important groups, most notably Thompson's group F. I will describe an algorithm to determine, for a finite set of elements in a "computable" subgroup of PL_o(I) (for example, F is computable), whether the group generated by this set is soluble, and if so, to determine its derived length.