Commensurators and Grigorchuk's groups (Clara Skowronek Santos, Complutense University of Madrid)

02.12.2025 10:30

The abstract commensurator of a group G is a generalization of its group of automorphisms. More concretely, it is a quotient of the set of almost automorphisms of G, that is, the set of isomorphisms between finite index subgroups of G. These commensurators have been studied for certain examples of groups, such as the first Grigorchuk group, and we are currently studying the commensurator of more groups of these family of Grigorchuk's groups.
C.E.Röver showed that the commensurator of the first Grigorchuk group G is the group generated by the Highman Thompson group G_2,1 and the group G itself. In this talk, I will discuss this commensurator and the one of the Grigorchuk-Erschler group, which can be obtained by similar techniques. I will also present some preliminary results about the automorphism group of a large subfamily of the family of Grigorchuk's groups, which we hope will be useful to compute their commensurators.
This is ongoing joint work with Alejandra Garrido.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 2.12.2025, Séminaire "Groupes et géométrie"

entrée libre