| Title:
|
On unit group of finite semisimple group algebras of non-metabelian groups up to order 72 (English) |
| Author:
|
Mittal, Gaurav |
| Author:
|
Sharma, Rajendra Kumar |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
429-455 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize the unit group of semisimple group algebras $\mathbb {F}_qG$ of some non-metabelian groups, where $F_q$ is a field with $q=p^k$ elements for $p$ prime and a positive integer $k$. In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group $((C_3\times C_3)\rtimes C_3)\rtimes C_2$ of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72. (English) |
| Keyword:
|
unit group |
| Keyword:
|
finite field |
| Keyword:
|
Wedderburn decomposition |
| MSC:
|
16U60 |
| MSC:
|
20C05 |
| idZBL:
|
Zbl 07442512 |
| idMR:
|
MR4336549 |
| DOI:
|
10.21136/MB.2021.0116-19 |
| . |
| Date available:
|
2021-11-08T16:20:30Z |
| Last updated:
|
2021-12-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149259 |
| . |
| Reference:
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