Productive elements in group cohomology. (Q542648)

Let \(G\) be a finite group and \(k\) be a field of characteristic \(p>0\). A nonzero cohomology class \(\zeta\in H^n(G,k)\), of degree \(n\geq 1\), is called productive if it annihilates the cohomology ring \(\text{Ext}^*_{kG}(L_\zeta,L_\zeta)\), where the \(kG\)-module \(L_\zeta\) is the kernel of the unique \(kG\)-module homomorphism \(\Omega^nk\to k\) associated to \(\zeta\). The aim of this paper is to study conditions for a cohomology class to be productive.