LetKbe a field which contains thed-th roots of unity. SupposeKhas characteristic 0 or char(K) ∤d. Letf(X) ∈K[X] be an irreducible and separable polynomial of degreemwith Galois group 𝔤. If 𝔤 acts doubly transitively on the set of roots off(Xd) and if the order of 𝔤 anddare relatively prime, then the Galois group off(Xd) over a splitting field off(X) is isomorphic towhered3|d2|d1|d. We prove that forthe Mathieu groupsand some other groups the same statement holds true for any. We further give equivalent interpretations ford1andd2.