We apply our results to determine by means of the action of WG on H∗(BT; IFp) the odd primes p for which H∗(BG; ZZ) has p-torsion. ams classification: 13A50 Invariant Theory, 55R40 Cohomology of Classifying Spaces, 57T10 Cohomology of Lie Groups
and identify it with the ideal J∞(WG)⊂ H∗(BT; IFp) of stable invariants of the Weyl group. We apply our results to determine by means of the action of WG on H∗(BT; IFp) the odd primes p for which H∗(BG; ZZ) has p-torsion. ams classification: 13A50 Invariant Theory, 55R40 Cohomology of Classifying Spaces, 57T10 Cohomology of Lie Groups