Non-triviality of Tate cohomology for certain classes of finite p-groups

Abstract

We prove that the Tate cohomology groups Ĥn(G∕Φ(G),Z(Φ(G))) are non-trivial, whenever G is a finite p-group of class 3, or the pth term of the upper central series of G contains Z(Φ(G)). This confirms a conjecture of Schmid for these groups. © 2017 Taylor & Francis.