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The unit groups of semisimple group algebras of some non-metabelian groups of order 144
- Source :
- Mathematica Bohemica, Vol 148, Iss 4, Pp 631-646 (2023)
- Publication Year :
- 2023
- Publisher :
- Institute of Mathematics of the Czech Academy of Science, 2023.
-
Abstract
- 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
- Subjects :
- unit group
finite field
wedderburn decomposition
Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 08627959 and 24647136
- Volume :
- 148
- Issue :
- 4
- Database :
- Directory of Open Access Journals
- Journal :
- Mathematica Bohemica
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.2e7f9cfbeb17495abd05eca61373b402
- Document Type :
- article
- Full Text :
- https://doi.org/10.21136/MB.2022.0067-22