On the congruence subgroup problem for branch groups Seminar

For any infinite group with a distinguished family of normal subgroups of finite index -- congruence subgroups-- one can ask whether every finite index subgroup contains a congruence subgroup. A classical example of this is the positive solution for SL(n,Z) where n>2, by Bass, Lazard and Serre. Groups acting on infinite rooted trees are a natural setting in which to ask this question. Branch groups, which are a particular family of groups acting on these trees, have a sufficiently nice subgroup structure to yield interesting results in this area. In the talk, I will introduce this family of groups and the congruence subgroup problem in this context and will present some recent results.