GGS-groups over primary trees: branch structures

We study branch structures in Grigorchuk–Gupta–Sidki groups (GGS-groups) over primary trees, that is, regular rooted trees of degree pn for a prime p. Apart from a small set of exceptions for p=2, we prove that all these groups are weakly regular branch over G′′. Furthermore, in most cases they are actually regular branch over γ3(G). This is a significant extension of previously known results regarding periodic GGS-groups over primary trees and general GGS-groups in the case n=1. We also show that, as in the case n=1, a GGS-group generated by a constant vector is not branch.