Explicit determination of generalized symmetric and alternating Galois groups

This paper shows a probabilistic algorithm to decide whether the Galois group of a given irreducible polynomial with rational coefficients is the generalized symmetric group Cp≀SmCp≀Sm or the generalized alternating group Cp≀AmCp≀Am. In the affirmative case, we give generators of the group with their action on the set of roots of the polynomial.