Group algebras of metacyclic groups over finite fields

Abstract

In this paper, we consider semisimple group algebras \({\mathbb {F}}_{q}G\) of non abelian split metacyclic groups over a finite field. We give conditions for them to have a minimal number of simple components and find the primitive central idempotents of \({\mathbb {F}}_{q}G\) in the case when the order G is equals \(p^{m}\ell ^{n}\), where p and \(\ell \) are different prime numbers.