Group of Units of Finite Group Algebras of Groups of Order 24

Abstract

Let $F$ be a finite field of characteristic $p$. The structures of the unit groups of group algebras over $F$ of the three groups $D_{24}$, $S_4$ and $SL(2, \mathbb{Z}_3)$ of order $24$ are completely described in \cite{K4, SM, SM1, FM, sh1}. In this paper, we give the unit groups of the group algebras over $F$ of the remaining groups of order $24$, namely, $C_{24}$, $C_{12} \times C_2$, $C_2^3 \times C_3$, $C_3 \rtimes C_8$, $C_3 \rtimes Q_8$, $D_6 \times C_4$, $C_6 \rtimes C_4$, $C_3 \rtimes D_8$, $C_3 \times D_8$, $C_3 \times Q_8$, $A_4 \times C_2$ and $D_{12} \times C_2$.