The Structure of the Unit Group of the Group Algebra
Canadian mathematical bulletin, Tome 54 (2011) no. 2, pp. 237-243

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2010-098-5
Mots-clés : 16U60, 16S34, 20C05, 15A33
Creedon, Leo; Gildea, Joe. The Structure of the Unit Group of the Group Algebra. Canadian mathematical bulletin, Tome 54 (2011) no. 2, pp. 237-243. doi: 10.4153/CMB-2010-098-5
@article{10_4153_CMB_2010_098_5,
     author = {Creedon, Leo and Gildea, Joe},
     title = {The {Structure} of the {Unit} {Group} of the {Group} {Algebra}},
     journal = {Canadian mathematical bulletin},
     pages = {237--243},
     year = {2011},
     volume = {54},
     number = {2},
     doi = {10.4153/CMB-2010-098-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-098-5/}
}
TY  - JOUR
AU  - Creedon, Leo
AU  - Gildea, Joe
TI  - The Structure of the Unit Group of the Group Algebra
JO  - Canadian mathematical bulletin
PY  - 2011
SP  - 237
EP  - 243
VL  - 54
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-098-5/
DO  - 10.4153/CMB-2010-098-5
ID  - 10_4153_CMB_2010_098_5
ER  - 
%0 Journal Article
%A Creedon, Leo
%A Gildea, Joe
%T The Structure of the Unit Group of the Group Algebra
%J Canadian mathematical bulletin
%D 2011
%P 237-243
%V 54
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-098-5/
%R 10.4153/CMB-2010-098-5
%F 10_4153_CMB_2010_098_5

[1] [1] Bovdi, A. A. and Szakács, A., A basis for the unitary subgroup of the group algebra of units in a finite commutative group algebra. Publ. Math. Debrecen 46(1995), no. 1–2, 97–120. Google Scholar

[2] [2] Bovdi, V. and Kovács, L. G., Unitary units in modular group algebras. Manuscr. Math. 84(1994), no. 1, 57–72. doi:10.1007/BF02567443 Google Scholar

[3] [3] Bovdi, V. and Rosa, A. L., On the order of the unitary subgroup of a modular group algebra. Comm. Algebra 28(2000), no. 4, 1897–1905. doi:10.1080/00927870008826934 Google Scholar

[4] [4] Bovdi, V., Konovalov, A., Rossmanith, R., and Schneider, C.. LAGUNA—Lie AlGebras and UNits of group Algebras. http://www.gap-system.org/Packages/laguna.html Google Scholar

[5] [5] Brooks, M., The Matrix reference Manual (online), 2005. http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/intro.html Google Scholar

[6] [6] Davis, P. J., Circulant matrices. John Wiley & Sons, New York-Chichester-Brisbane, 1979. Google Scholar

[7] [7] Creedon, L., The unit group of small group algebras and the minimum counterexample to the isomorphism problem. Int. J. Pure Appl. Math. 49(2008), no. 4, 531–537. Google Scholar

[8] [8] Gildea, J., On the order of . Int. J. Pure Appl. Math. 46(2008), no. 2, 267–272. Google Scholar

[9] [9] Hurley, T., Group rings and rings of matrices. Int. J. Pure Appl. Math. 31(2006), no. 3, 319–335. Google Scholar

[10] [10] Milies, C. Polcino and Sehgal, S. K., An introduction to group rings. Algebras and Applications, 1, Kluwer Academic Publishers, Dordrecht, 2002. Google Scholar

[11] [11] Sandling, R., Units in the modular group algebra of a finite abelian p-group. J. Pure Appl. Algebra 33(1984), no. 3, 337–346. doi:10.1016/0022-4049(84)90066-5 Google Scholar

[12] [12] Sandling, R., Presentations for units groups of modular group algebras of groups of order 16 . Math. Comp. 59(1992), no. 200, 689–701. Google Scholar

[13] The GAP Group, GAP—groups, algorithms, programming. Version 4.4.10, 2007. http://www.gap-system.org Google Scholar

Cité par Sources :