Geodesic
Explicit Classifications of Some 2-Extensions of a Field of Characteristic Different from 2
Canadian journal of mathematics, Tome 42 (1990) no. 5, pp. 825-855

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Let p be a prime number. Let k be a field of characteristic different from p and containing the p-th roots of unity. Let be a finite group. Let L/k be a finite normal extension with Galois group and let c be a 2-cocycle on with coefficients in , where acts trivially on By Emb(L/k, c) we denote the question of the existence of a finite normal extension M of k, such that M contains L, such that [M: L] = p, and such that, denoting by the Galois group of M/k, the extension is given by the class of c. 
Kiming, Ian. Explicit Classifications of Some 2-Extensions of a Field of Characteristic Different from 2. Canadian journal of mathematics, Tome 42 (1990) no. 5, pp. 825-855. doi: 10.4153/CJM-1990-043-6
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