Abstract: The automorphism group of a d-adic rooted tree Aut(T) is isomorphic to the infinitely iterated wreath of copies of the symmetric group Sym(d) w.r.t. the imprimitive action. The group Aut(T) has several interesting subgroups, e.g. Grigorchuk and Gupta-Sidki groups. These are examples of just infinite groups, i.e. groups that are infinite and each of their proper quotients is finite.
On the other hand, there is another natural action of the wreath product, i.e. the product action, and we can consider infinitely iterated wreath products w.r.t. the product action (IIWPPA for short).
On the other hand, there is another natural action of the wreath product, i.e. the product action, and we can consider infinitely iterated wreath products w.r.t. the product action (IIWPPA for short).
In this talk I will present some work in progress on abstract subgroups of IIWPPA and some structures they preserve. Finally, I will hint at how these ideas could be used to produce new examples of (hereditarily) just infinite groups.