Rostyslav Kravchenko: On the lattice of subgroups of the lamplighter group

We study the lattice of subgroup of the Lamplighter groups (Z/pZ)^n \wr Z, in particular what are maximal, weakly maximal subgroups, what subgroups are closed in the pro-p topology, etc. We apply it to the study of the relative gradient rank. This is joint work with R. Grigorchuk.