  The subgroup induction property is a property of self-similar groups acting
on rooted trees introduced by Grigorchuk and Wilson in 2003 that appears to
have strong implications on the structure of the groups possessing it. It was
for example used in the proof that the first Grigorchuk group as well as the
Gupta-Sidki 3-group are subgroup separable (locally extended residually finite)
or to describe their finitely generated subgroups as well as their weakly
maximal subgroups. However, until now, there were only two known examples of
groups with this property, namely 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 for branch groups, a
particularly interesting class of self-similar groups. Notably, we show that
finitely generated branch groups with the subgroup induction property must be
torsion, just infinite and subgroup separable, and we establish conditions
under which all their maximal subgroups are of finite index and all their
weakly maximal subgroups are closed in the profinite topology. Then, we show
that every torsion GGS group has the subgroup induction property, hence
providing the first infinite family of examples of groups with this property.
