Galois realizability of non-split group extensions of \(C_{2}\) by (\(C_{2})^{r}\times (C_{4})^{s}\times (D_{4})^{t}\).
The paper under review considers embedding problems of field extensions given by an exact sequence \(1\rightarrow C_2\rightarrow G\rightarrow (C_2)^r\times (C_4)^s\times (D_4)^t\rightarrow 1\), where \(C_2,C_4\) are cyclic groups of order 2, resp.~4 and \(D_4\) denotes the dihedral group of order 8. Theorem 1 gives the obstruction to this embedding problem in terms of tensor products of quaternion algebras defined by certain subfields. As an application we get obstructions to the realizability of 13 groups of order 32 which were not previously known.
scientific article; zbMATH DE number 2055637
scientific article