Geodesic
Unit groups of group algebras of some small groups
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 149-157 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $FG$ be a group algebra of a group $G$ over a field $F$ and ${\mathcal U}(FG)$ the unit group of $FG$. It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group $G$ with order $21$ over any finite field of characteristic $3$ is established. We also characterize the structure of the unit group of $FA_4$ over any finite field of characteristic $3$ and the structure of the unit group of $FQ_{12}$ over any finite field of characteristic $2$, where $Q_{12}=\langle x, y; x^6=1, y^2=x^3, x^y=x^{-1} \rangle $.
Let $FG$ be a group algebra of a group $G$ over a field $F$ and ${\mathcal U}(FG)$ the unit group of $FG$. It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group $G$ with order $21$ over any finite field of characteristic $3$ is established. We also characterize the structure of the unit group of $FA_4$ over any finite field of characteristic $3$ and the structure of the unit group of $FQ_{12}$ over any finite field of characteristic $2$, where $Q_{12}=\langle x, y; x^6=1, y^2=x^3, x^y=x^{-1} \rangle $.
DOI : 10.1007/s10587-014-0090-0
Classification : 16S34, 16U60, 20C05
Keywords: group ring; unit group; augmentation ideal; Jacobson radical 
@article{10_1007_s10587_014_0090_0,
     author = {Tang, Gaohua and Wei, Yangjiang and Li, Yuanlin},
     title = {Unit groups of group algebras of some small groups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {149--157},
     year = {2014},
     volume = {64},
     number = {1},
     doi = {10.1007/s10587-014-0090-0},
     mrnumber = {3247451},
     zbl = {06391483},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0090-0/}
}
TY  - JOUR
AU  - Tang, Gaohua
AU  - Wei, Yangjiang
AU  - Li, Yuanlin
TI  - Unit groups of group algebras of some small groups
JO  - Czechoslovak Mathematical Journal
PY  - 2014
SP  - 149
EP  - 157
VL  - 64
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0090-0/
DO  - 10.1007/s10587-014-0090-0
LA  - en
ID  - 10_1007_s10587_014_0090_0
ER  - 
%0 Journal Article
%A Tang, Gaohua
%A Wei, Yangjiang
%A Li, Yuanlin
%T Unit groups of group algebras of some small groups
%J Czechoslovak Mathematical Journal
%D 2014
%P 149-157
%V 64
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0090-0/
%R 10.1007/s10587-014-0090-0
%G en
%F 10_1007_s10587_014_0090_0
Tang, Gaohua; Wei, Yangjiang; Li, Yuanlin. Unit groups of group algebras of some small groups. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 149-157. doi: 10.1007/s10587-014-0090-0

Cité par Sources :