\({\mathbb{Q}}\)-admissibility of certain nonsolvable groups (Q1100510)

The author shows that there exists a finite dimensional central division algebra D over the field of rational numbers such that a maximal subfield of D is a Galois extension of \({\mathbb{Q}}\) with Galois group isomorphic to a central extension of \({\mathbb{Z}}_ 2\) by \(S_ 5.\) As a corollary the author shows that every finite Sylow-metacyclic group which has \(A_ 5\) as a composition factor can appear as a Galois group in a similar fashion.