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