| Title:
|
The unit groups of semisimple group algebras of some non-metabelian groups of order $144$ (English) |
| Author:
|
Mittal, Gaurav |
| Author:
|
Sharma, Rajendra Kumar |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
631-646 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider all the non-metabelian groups $G$ of order $144$ that have exponent either $36$ or $72$ and deduce the unit group $U(\mathbb {F}_qG)$ of semisimple group algebra $\mathbb {F}_qG$. Here, $q$ denotes the power of a prime, i.e., $q=p^r$ for $p$ prime and a positive integer $r$. Up to isomorphism, there are $6$ groups of order $144$ that have exponent either $36$ or $72$. Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order $144$ that are a direct product of two nontrivial groups. In all, this paper covers the unit groups of semisimple group algebras of $17$ non-metabelian groups.\looseness -1 (English) |
| Keyword:
|
unit group |
| Keyword:
|
finite field |
| Keyword:
|
Wedderburn decomposition |
| MSC:
|
16U60 |
| MSC:
|
20C05 |
| DOI:
|
10.21136/MB.2022.0067-22 |
| . |
| Date available:
|
2023-11-23T12:41:51Z |
| Last updated:
|
2023-11-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151979 |
| . |
| Reference:
|
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