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