The mod p cohomology rings of the nonabelian split metacyclic p-groups (Q799817)

Let G be a nonabelian group with split extension \(C_{p^ m}\mapsto G\twoheadrightarrow C_{p^ n}\) and let k denote the field with p elements. We use the associated spectral sequence to compute the cohomology rings \(H^*(G,k)\). There are essentially two classes of cohomology rings depending on the dimension of \(H^ 2(G,k)\). In the case \(p=2\) we need additional spectral sequences to calculate the relations in \(H^*(G,k)\).