Totally nonfree actions and infinite symmetric group
  We consider the totally nonfree (TNF) action of a groups and the corresponding adjoint invariant (AD) measures on the 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 $S_{\Bbb N}$. The problem is closely related to the theory of characters and factor representations of groups. 
Anatoly Vershik
math.DS math.RT