ИСТИНА

In a number of papers it was shown that the Poincar\'e series of some natural filtrations (defined by valuations) on the rings of germs of functions on singularities are related (sometimes coincide) with appropriate monodromy zeta functions. A generalization of these results to cases equivariant with respect to an action of a finite group $G$ could help to understand reasons for these relations. One meets the problem of the lack of appropriate definitions of equivariant versions of Poincar\'e series and monodromy zeta functions. Recently such version were defined as elements of Grothendieck rings of $G$-sets with some additional structures. We shall discuss these approaches and some results obtained on this way.