The structure of the unit group of the group algebra $F(C_3 \times D_{10})$

TL;DR

This paper determines the structure of the unit group of the group algebra over any finite field of characteristic not equal to 3, extending previous results limited to characteristic 3.

Contribution

It generalizes the known structure of the unit group of the group algebra for $F(C_3 imes D_{10})$ from characteristic 3 to all characteristics not equal to 3.

Findings

Structure of $U(F(C_3 imes D_{10}))$ over any finite field of characteristic $p eq 3$

Extension of previous characteristic 3 results

Provides explicit description of the unit group structure

Abstract

Let $D_{n}$ be the dihedral group of order $n$. The structure of the unit group $U(F(C_3 \times D_{10}))$ of the group algebra $F(C_3 \times D_{10})$ over a finite field $F$ of characteristic $3$ is given in \cite{sh13}. In this article, the structure of $U(F(C_3 \times D_{10}))$ is obtained over any finite field $F$ of characteristic $p \neq 3$.