Weakly maximal subgroups in regular branch groups
Abstract Let G be a finitely generated regular branch group acting by automorphisms on a regular rooted tree T It is well known that stabilizers of infinite rays in T (aka parabolic subgroups) are weakly maximal subgroups in G that is, maximal among subgroups of infinite index. We show that, given a finite subgroup Q G G possesses uncountably many automorphism equivalence classes of weakly maximal subgroups containing Q In particular, for Grigorchuk Gupta Sidki type groups this implies that they have uncountably many automorphism equivalence classes of weakly maximal subgroups that are not parabolic.