THE STRUCTURE OF THE UNITARY UNITS OF THE GROUP ALGEBRA F2kD8

Year 2011, Volume: 9 Issue: 9, 171 - 176, 01.06.2011

Joe Gildea

Abstract

The structure of the unitary unit group of the group algebra of the dihedral group of order 8 over any finite field of characteristic 2 is established.

Keywords

group ring, group algebra, unitary unit group, dihedral group

References

• A.A. Bovdi and L. Erdei, Unitary units in the modular group algebra of groups of order 16, Technical Reports Debrecen, 94/4 (1996), 57–72.
• V.A. Bovdi and L.G. Kov´acs, Unitary units in modular group algebras, Manuscr. Math., 84(1) (1994), 57–72.
• V. Bovdi and A.L. Rosa, On the order of the unitary subgroup of a modular group algebra, Comm. Algebra, 28(4) (2000), 1897–1905.
• A.A. Bovdi and A. Szak´acs, Unitary subgroup of the group of units of a modular group algebra of a finite abelian p-group, Math. Zametki, 45(6) (1989), 23–29.
• L.Creedon and J. Gildea, The Structure of the unit group of the group alge- bra F2kD, Canad. Math. Bull., Published electronically on August 26, 2010. doi:10.4153/CMB-2010-098-5.
• L.Creedon and J. Gildea, Unitary units of the group algebra F2kQ8, Internat. J. Algebra Comp., 19(2) (2009), 283–286.
• P.J. Davis, Circulant Matrices, Chelsea Publishing, New York, 1979.
• J. Gildea, On the order of U(FpkD2p), Int. J. Pure Appl. Math., 46(2) (2008), –272.
• T. Hurley, Group rings and rings of matrices, Int. J. Pure Appl. Math., 31 (2006), 319–335.
• C. Polcino Milies and S.K. Sehgal, An Introduction to Group Rings (Algebras and Applications), Kluwer Academic Publishers, Dordrecht, 2002.
• R. Sandling, Units in the modular group algebra of a finite abelian p-group, J. Pure Appl. Algebra, 33 (1984), 337–346.
• R. Sandling, Presentations for units groups of modular group algebras of groups of order 16, Math. Comp., 59 (1992), 689–701. Joe Gildea
• Department of Mechanical and Electronic Engineering School of Engineering Institute of Technology Sligo Ireland e-mail: [e-mail]