The Structure of the Unit Group of the Group Algebra ${\mathbb{F}}_{2^k}D_{8}$

http://dx.doi.org/10.4153/CMB-2010-098-5
Canad. Math. Bull. 54(2011), 237-243

  Published:2010-08-26
 Printed: Jun 2011

Let $RG$ denote the group ring of the group $G$ over the ring $R$. Using an isomorphism between $RG$ and a certain ring of $n \times n$ matrices in conjunction with other techniques, the structure of the unit group of the group algebra of the dihedral group of order $8$ over any finite field of chracteristic $2$ is determined in terms of split extensions of cyclic groups.