Commensurated subgroups in finitely generated branch groups
Abstract A subgroup H G {H\leq G} is commensurated if H H g H g 1 |H:H\cap gHg^ 1}\infty$ for all g G {g\in G} We show that a finitely generated branch group is just infinite if and only if every commensurated subgroup is either finite or of finite index. As a consequence, every commensurated subgroup of the Grigorchuk group and many other branch groups of independent interest is either finite or of finite index.