Seminario Teoría de Grupos
On the BNS Invariant
Ponente: Javier Pavez (Universidad de Chile)Fecha: jueves 09 de julio de 2026 - 11:30Lugar: Aula Gris 1, ICMAT
Resumen:
A naïve question one can ask about a finitely generated group is whether or not all its subgroups are finitely generated. This is true for abelian, nilpotent and polyclic groups, but not for all groups, since the free group in two generators and its derived group provide a famous counterexample. A less naïve question is whether or not we can provide some criteria to check if a subgroup is finitely generated. Personally, I'm not aware of a method that would work for any class of subgroup, but since the 80's, there's one for normal subgroups of abelian quotient provided by a group invariant developed by Bieri, Neumann and Strebel. In this talk I will explain the necessary preeliminaries to construct said invariant and criteria, and if time permits, some ideas on how to broaden the class of subgroups that this method admits by the use of total left-invariant preorders on a group, and how these techniques interact with the established theory.
