Units in $F{D}_{2p}$

Abstract

In this paper, we present the structure of the group of *-unitary units in the group algebra $F{D}_{2p}$, where $F$ is a finite field of characteristic $p>2$, $D_{2p}$ is the dihedral group of order $2p$, and * is the canonical involution of the group algebra $F{D}_{2p}$. We also provide the structure of the maximal $p$-subgroup of the unit group $\mathcal{U}(F{D}_{2p})$ and compute a basis of its center.

15 pages