Anitha Thillaisundaram

Maximal subgroups of groups acting on rooted trees

Groups acting on rooted trees, especially the so-called branch groups, have been vastly studied over the past few decades, owing to their exotic properties - in particular, branch groups have been used to answer important open problems and disprove conjectures. The study of maximal subgroups of branch groups has recently picked up speed, with new developments by Francoeur enabling one to study the maximal subgroups of the larger class of weakly branch groups. A prominent example of a weakly branch, but not branch, group is the Basilica group. This was the first example of an amenable group which is not subexponentially amenable. In this talk, I will present results concerning maximal subgroups of a family of generalised Basilica groups. This is joint work with Karthika Rajeev.