Nilpotency degree of integral cohomology classes of p-groups

摘要

Let p be a prime number and let G be a p-group which is not elementary abelian. For every integral cohomology class $ xi $ of G which restricts trivially to all proper subgroups, we show that $ xi^{p} = 0 $ if p > 2 or $ textrm{deg}(xi) $ is even, and $ xi^{3} = 0 $ if p = 2 and $ textrm{deg}(xi) $ is odd. This result is applied to get an upper bound, which is $ frac{|G|}{p} $ , for the nilpotence degrees of nilpotent integral cohomology classes of G.