Seminario Teoría de Grupos
Commensurators of free groups and free pro-p groups
Ponente: Adrien Le Boudec (ENS Lyon)Fecha: miércoles 11 de diciembre de 2024 - 15:00Lugar: Sala Naranja (ICMAT)
Resumen:
The commensurator Comm(Gamma) of a group Gamma is the group of isomorphisms between finite index subgroups of Gamma modulo coincidence on a finite index subgroup. The commensurator Comm(G) of a profinite group G is defined similarly, except that we consider finite index open subgroups. The group Comm(G) plays a central role in the study of locally compact groups that are locally isomorphic to G. I will survey recent results notably regarding simplicity of some natural open subgroups of Comm(G) for G a finitely generated free pro-p group, and
also of some subgroups of Comm(F) for F a finitely generated free (abstract) group. Joint with Yiftach Barnea, Mikhail Ershov, Colin Reid, Matteo Vannacci, Thomas Weigel.
