×

The structure of the unit group of the group algebra \(F_{2^k}A_4\). (English) Zbl 1237.16035

Using the split extensions of cyclic groups, the structure of the unit group of the group algebra of the group \(A_4\) over any finite field of characteristic \(2\) is described.

MSC:

16U60 Units, groups of units (associative rings and algebras)
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S34 Group rings
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] A.A. Bovdi, L. Erdei: Unitary units in the modular group algebra of groups of order 16. Technical Reports Debrecen 96/4. 1996, pp. 57–72.
[2] A.A. Bovdi, A. Szakács: Unitary subgroup of the group of units of a modular group algebra of a finite abelian p-group. Math. Zametki 45 (1989), 23–29. · Zbl 0674.16007
[3] V.A. Bovdi, L.G. Kovács: Unitary units in modular group algebras. Manuscr. Math. 84 (1994), 57–72. · Zbl 0816.16027
[4] V. Bovdi, A. L. Rosa: On the order of the unitary subgroup of a modular group algebra. Commun. Algebra 28 (2000), 1897–1905. · Zbl 0952.16022
[5] L. Creedon, J. Gildea: The structure of the unit group of the group algebra F. Can. Math. Bull 54 (2011), 237–243. doi:10.4153/CMB-2010-098-5. · Zbl 1242.16033
[6] L. Creedon, J. Gildea: Unitary units of the group algebra F. Internat. J. Algebra Comput. 19 (2009), 283–286. · Zbl 1171.16302
[7] P. J. Davis: Circulant Matrices. Chelsea Publishing, New York, 1979.
[8] T. Hurley: Group rings and rings of matrices. Int. J. Pure Appl. Math. 31 (2006), 319–335. · Zbl 1136.20004
[9] C. Polcino Milies, S.K. Sehgal: An Introduction to Group Rings. Kluwer Academic Publishers, Dordrecht, 2002. · Zbl 0997.20003
[10] R. Sandling: Units in the modular group algebra of a finite abelian p-group. J. Pure Appl. Algebra 33 (1984), 337–346. · Zbl 0543.20008
[11] R. Sandling: Presentations for units groups of modular group algebras of groups of order 16. Math. Comp. 59 (1992), 689–701. · Zbl 0784.16021
[12] R.K. Sharma, J.B. Srivastava, M. Khan: The unit group of FA 4. Publ. Math. Debrecen 71 (2007), 21–26. · Zbl 1135.16033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.