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In this article, we show explicitly the Wedderburn decomposition of themetacyclic group algebra $\mathbb F_qG$, where $G$ has a cyclic subgroup ofindex 2 and $\gcd(|G|,q)=1$. We also construct the complete set of central andleft idempotents of these group algebras.

Wedderburn Decomposition and Idempotents of some finite metacyclic group algebras