Group Extensions and Cohomology Groups Original Research Article

Let q ≥ 2 be an integer and let G be a finite group which is assumed to have odd order if q ≥ 3. We show that there is a finite group extension image of G with abelian kernel. image depending on q, such that the inflation map inf: Hq(G, image/image) → Hq(image, image/image) is trivial. For q = 2 our construction yields a representation group image for G in the sense of I. Schur.