  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.
