Units in $F_{2^k}D_{2n}$

Abstract

Let $F_q D_{2n}$ be the group algebra of $D_{2n}$, the dihedral group of order $2n$ over $F_q=GF(q)$. In this paper, we establish the structure of $U(F_{2^k}D_{2n})$, the unit group of $F_{2^k}D_{2n}$ and that of its normalized unitary subgroup $V_*(F_{2^k}D_{2n})$ with respect to canonical involution $*$ when $n$ is odd.

Keywords

• Group Algebra
• Unit Group
• Unitary Units