| Title:
|
Unit groups of group algebras of some small groups (English) |
| Author:
|
Tang, Gaohua |
| Author:
|
Wei, Yangjiang |
| Author:
|
Li, Yuanlin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
149-157 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $. (English) |
| Keyword:
|
group ring |
| Keyword:
|
unit group |
| Keyword:
|
augmentation ideal |
| Keyword:
|
Jacobson radical |
| MSC:
|
16S34 |
| MSC:
|
16U60 |
| MSC:
|
20C05 |
| idZBL:
|
Zbl 06391483 |
| idMR:
|
MR3247451 |
| DOI:
|
10.1007/s10587-014-0090-0 |
| . |
| Date available:
|
2014-09-29T09:46:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143956 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
