Totally nonfree actions and the infinite symmetric group

We consider totally nonfree (TNF) actions of groups and the corresponding adjoint invariant (AD) measures on lattices of the subgroups of the given group. The main result is the description of all adjoint-invariant and TNF measures on the lattice of subgroups of the infinite symmetric group $S_\mathbb N$. The problem is closely related to the theory of characters and factor representations of groups.