Group Extensions and Cohomology Groups

AbstractLet 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 G̃ of G with abelian kernel. G̃ depending on q, such that the inflation map inf: Hq(G, Q/Z) → Hq(G̃, Q/Z) is trivial. For q = 2 our construction yields a representation group G̃ for G in the sense of I. Schur