Hilbert series of PI relatively free G-graded algebras are rational functions

Eli Aljadeff, Alexei Kanel-Belov

Let G be a finite group, (g_{1},...,g_{r}) an (unordered) r-tuple of G^{(r)} and x_{i,g_i}'s variables that correspond to the g_i's, i=1,...,r. Let F<x_{1,g_1},...,x_{r,g_r}> be th…