Explicit determination of generalized symmetric and alternating Galois groups (Q861846)

In trying to understand how the (center of) the Galois group \(\text{Gal}_{\mathbb Q} f\) of an irreducible polynomial \(f(x) \in \mathbb Q [x]\) acts on the zeros of \(f\), the author of the paper under review is led to consider polynomials \(f\) for which \(\text{Gal}_{\mathbb Q} f\) is the wreath product \(C_p \wr S_m\) or \(C_p \wr A_m\), where \(C_p\) is cyclic of prime order \(p\) and where \(S_m\) and \(A_m\) are the symmetric and alternating groups of degree \(m\). He describe a method for determining whether \(\text{Gal}_{\mathbb Q} f\), for a given \(f\), is of one of these types. When it is, a set of generators of \(\text{Gal}_{\mathbb Q} f\) together with their actions on the zeros of \(f\) are given.