Subgroup induction property for branch groups

Abstract

Recently, the so-called subgroup induction property attracted the attention of mathematicians working with branch groups. It was for example used to prove that groups with this property are subgroup separable (locally extensively residually finite) or to describe their finitely generated subgroups as well as their weakly maximal subgroups. Alas, until now, there were only two know examples of groups with this property: the first Grigorchuk group and the Gupta-Sidki 3-group.The aim of this article is twofold. First, we investigate various consequences of the subgroup induction property, such as being just infinite or having all maximal subgroups of finite index. Then, we show that every torsion GGS group has the subgroup induction property, hence providing infinitely many new examples.