Journal of the
Korean Mathematical Society JKMS

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 char\,${\mathbb K}$ does not divide $|G|$ but there is no assumption made of ${\mathbb K}$ being algebraically closed.

Keywords: finite group, semidirect product, representations, induced modules, irreducibility

MSC numbers: 20C20, 20D99