Nilpotence in Group Cohomology

We study bounds on nilpotence in H*(BG), the mod p cohomology of the classifying space of a compact Lie group G. Part of this is a report of our previous work on this problem, updated to reflect the consequences of Peter Symonds recent verification of Dave Benson’s Regularity Conjecture. New results are given for finite p–groups, leading to good bounds on nilpotence in H*(BP) determined by the subgroup structure of the p–group P.