  We show how the classification of simple singularities of functions can be
reduced directly, not using the normal forms, to the classification of
irreducible Weyl groups. We also prove that the class of a singularity in its
local algebra always belongs to the tangent cone to the stratum $\mu =const$ of
the singularity. An interesting characterization of Coxeter elements among
quasi-Coxeter elements of a Weyl group (of one of the types A-D-E) is found.
