Abstract.
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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Eingegangen am 8. 12. 2000
Rights and permissions
About this article
Cite this article
Minh, P. Nilpotency degree of integral cohomology classes of p-groups. Arch. Math. 79, 328–334 (2002). https://doi.org/10.1007/PL00012454
Issue Date:
DOI: https://doi.org/10.1007/PL00012454