Unit Groups of group algebras of certain quasidihedral group

Abstract

Let $F_{q}$ be any finite field of characteristic $p>0$ having $q = p^{n}$ elements. In this paper, we have obtained the complete structure of unit groups of group algebras $F_{q}[QD_{2^k}]$, for $k = 4$ and $5$, for any prime $p>0$, where $QD_{2^k}$ is quasidihedral group of order $2^k$