  We prove that if an ultrafilter L is not coherent to a Q-point, then each
analytic non-sigma-bounded topological group G admits an increasing chain <G_a
: a < b(L)> of its proper subgroups such that: (i) U_{a in b(L)} G_a=G; and
$(ii)$ For every sigma-bounded subgroup H of G there exists a such that H is a
subset of G_a. In case of the group Sym(w) of all permutations of w with the
topology inherited from w^w this improves upon earlier results of S. Thomas.
