Group extensions and cohomology groups
Let \(q\geq 2\) be an integer and let G be a finite group which is assumed to have odd order if \(q\geq 3\). We show that there is a finite group extension \(\tilde G\) of G with abelian kernel such that the inflation map inf: \(H^ q(G,{\mathbb{Q}}/Z)\to H^ q(\tilde G,{\mathbb{Q}}/Z)\) is trivial. For \(q=2\) our construction yields a representation group \(\tilde G\) for G in the sense of I. Schur. The proof makes use of basic results of algebraic number theory and class field theory.
scientific article; zbMATH DE number 4192002