Maximal subgroups of infinite index in branch groups (Jorge Fariña Asategui, Université de Genève)

17.09.2026 13:00 – 14:00

A finitely generated infinite group may or may not admit maximal subgroups of infinite index. For certain families of groups, such as linear groups, it is completely characterised when they admit maximal subgroups of infinite index. For the class of branch groups, it was Bondarenko who constructed the first example admitting maximal subgroups of infinite index. These groups are very special, as they contain copies of themselves. Apart from these groups, which always act on regular rooted trees of degree at least 5, there is only one example of a branch group with maximal subgroups of infinite index, which acts on the binary rooted tree. In particular, there is no example acting on a regular rooted tree of degree 3 or 4.

In this talk, we introduce a new construction which produces an infinite family of branch groups with maximal subgroups of infinite index and acting on regular rooted trees of any degree. This is joint work with Anitha Thillaisundaram.

Lieu

Room 1-05, ATT. NEW SCHEDULE, Séminaire "Groupes et géométrie"

entrée libre