Maximal subgroups in torsion branch groups

We study the maximal subgroups of branch groups and obtain a criterion that ensures that certain spinal groups are contained in the class MF of groups with all maximal subgroups of finite index. This allows us to construct branch groups within MF exhibiting novel properties, for example, groups that possess non-normal maximal subgroups. Furthermore, we give new concrete examples of branch groups outside MF , with explicitly given maximal subgroups of infinite index. Most prominently, we construct a periodic branch group outside MF .