Title: Polynomial ideals and classes of finite groups.
Author: Serge Bouc.
Abstract: The object of this note is to discuss properties of some polynomials (on a countable set of indeterminates) attached to any finite group, which generalize the Eulerian functions of a group defined by P. Hall. In particular, I define some classes of finite groups associated to prime ideals of the polynomial ring, and I show that each finite group has a unique largest quotient in such a class of groups.