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A classical result of Artin states that the ideal generated by symmetricpolynomials in $n$ variables is of codimension $n!$. The author, F. Bergeronand N. Bergeron have recently obtained a surprising analogous in the case ofquasi-symmetric polynomials. In this case, the ideal is of codimension given by$C_n$, the $n$-th Catalan number. Quasi-symmetric polynomials are theinvariants of a certain action of the symmetric group $S_n$ defined by F.Hivert. The aim of this work is to generalize these results to the wreathproduct $S_n\wr \Z_m$, also known as the generalized symmetric group $G\nm$. Wefirst define a quasi-symmetrizing action of $G\nm$ on $\C[x_1,...,x_n]$, thenobtain a description of the invariants and the codimension of the associatedideal, which is $m^n C_n$.

Polyn\^omes quasi-invariants et super-coinvariants pour le groupe sym\'etrique g\'en\'eralis\'e