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Journals / Journal of Algebra Combinatorics Discrete Structures and Applications / 2021 / Cilt: 8 - Sayı: 2

On unit group of finite semisimple group algebras of non-metabelian groups of order 108

Gaurav MİTTAL
Rajendra. K. SHARMA
Pages
59–71
Publication Date
2021-05-20
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

And as a by-product obtain the unit groups.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we characterize the unit groups of semisimple group algebras $\mathbb{F}_qG$ of non-metabelian groups of order $108$, where $F_q$ is a field with $q=p^k$ elements for some prime $p > 3$ and positive integer $k$.
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Key Findings & Data:Up to isomorphism, there are $45$ groups of order $108$ but only $4$ of them are non-metabelian.
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Conclusion & Impact:And as a by-product obtain the unit groups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Unit group · Finite field · Wedderburn decomposition

Abstract

In this paper, we characterize the unit groups of semisimple group algebras $\mathbb{F}_qG$ of non-metabelian groups of order $108$, where $F_q$ is a field with $q=p^k$ elements for some prime $p > 3$ and positive integer $k$. Up to isomorphism, there are $45$ groups of order $108$ but only $4$ of them are non-metabelian. We consider all the non-metabelian groups of order $108$ and find the Wedderburn decomposition of their semisimple group algebras. And as a by-product obtain the unit groups.

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Cite This Article

MİTTAL, G., SHARMA, R. K. (2021). On unit group of finite semisimple group algebras of non-metabelian groups of order 108. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 8 - Sayı: 2, 59–71. https://ajindex.com/articles/861496

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