Abstract A Grigorchuk–Gupta–Sidki (GGS)-group is a subgroup of the automorphism group p -regular rooted tree for an odd prime , generated by one and directed automorphism. Pervova proved that all torsion GGS-groups do not have maximal subgroups infinite index. Here, we extend result to nontorsion GGS-groups, which include weakly regular branch, but GGS-group.

THIS paper concerns maximal subgroups of symmetric groups on infinite, usually countable, sets. Our main aim is to give examples of maximal subgroups which could claim to be almost stabilisers of familiar combinatorial structures. We emphasise that maximal subgroup always means maximal proper subgroup. Throughout this paper, Cl will denote an infinite set, usually countable. The power set of Q ...