On irreducibility of induced modules and an adaptation of the Wigner--Mackey method of little groups

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group $G$ over a field ${\mathbb K}$ where the group $G$ is a semidirect product of a normal abelian subgroup $N$ and a subgroup $H$. The main results are proved with the assumption that ${\rm char} {\mathbb K}$ does not divide $|G|$ but there is no assumption made of ${\mathbb K}$ being algebraically closed.