Explicit idempotents of finite group algebras

Let ${\mathbb{F}}_q$ be a finite field with $q$ elements, $G$ a finite cyclic group of order $p^k$ and $p$ is an odd prime with $\mathrm{g}\mathrm{c}\mathrm{d}(q,p)=1$. In this article, we determine an explicit expression for the primitive idempotents of ${\mathbb{F}}_{q}G$. This result extends the result in Arora-Pruthi [1] and Sharma-Bakshi-Dumir-Raka [8].