Invariants for the computation of intransitive and transitive Galois groups

One hard step in the computation of Galois groups by Stauduhar’s method is the construction of relative invariants. In this note, a representation-theoretic approach is given for the construction in the case of an intransitive group.In the second part of the article, it is shown that the construction can be used for groups that have a suitable intransitive subgroup. The construction solves an open question of Fieker and Klüners.