On subgroup structure of groups of branch type (Rostislav Grigorchuk, Texas A&M)

14.03.2023 10:30

Groups of branch type is a remarkable class of groups full of groups with unusual properties and related to numerous branches of mathematics. Some of these groups bear intriguing names like Hanoi Towers Groups, Basilica, IMG(z^2+i), ....
This class contains groups of intermediate growth (between polynomial and exponential), amenable but not elementary amenable groups, groups of Burnside type (i.e., infinite finitely generated torsion groups), just-infinite groups, finitely constrained groups etc.
Also, groups of branch type have unusual structure of the lattice of subgroups. In my talk, first, I will give a panorama of known results about subgroups of branch (and weakly branch) groups, focusing on maximal and weakly maximal subgroups and subgroup separability (or LERF) property. Then I will discuss the block structure of finitely generated subgroups and related topics. Most of the results presented in the talk were obtained by the speaker during his visits to Geneva in joint works with L .Bartholdi, T. Nagnibeda, P-H. Leemann and D. Francoeur.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 14.03.2023, Séminaire "Groupes et géométrie"

entrée libre