Universally solvable embedding problems (Q809142)

Let \(k\) be a field and \(K\) a Galois algebra over \(k\) with Galois group \(G\) isomorphic to a group \(F\). The embedding problem connected with the exact sequence \(1\to A\to G\to F\to 1\) is called universally solvable if it is solvable for any extension \(K/k\) with given group \(F\). The author gives examples of universally solvable embedding problems.