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

Published:2010-08-26
Printed: Jun 2011
• Leo Creedon,
School of Engineering, Institute of Technology, Sligo, Ireland
• Joe Gildea,
School of Engineering, Institute of Technology, Sligo, Ireland
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## Abstract

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.
 MSC Classifications: 16U60 - Units, groups of units 16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings 20C05 - Group rings of finite groups and their modules [See also 16S34] 15A33 - Matrices over special rings (quaternions, finite fields, etc.)
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