The relative Heller operator and relative cohomology for the Klein 4-group

Let G be the Klein four-group and let k an arbitrary field of characteristic 2. A classification indecomposable kG-modules is known. We calculate relative cohomology groups Hχi(G,N) for every kG-module N, where χ set proper subgroups in G. This extends work Pamuk Yalcin to with non-trivial coefficients. also show that all cup products strictly positive degree Hχ*(G,k) are trivial.