In order to complement the abstract theory of the paper, we deduce the Wedderburn decomposition and hence the unit group of semisimple group algebra $\mathbb{F}_q(A_5\rtimes C_4)$, where $A_5\rtimes C_4$ is a non-metabelian group and $C_4$ is a cyclic group of order $4$.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we derive a condition under which the Wedderburn decomposition of a semisimple group algebra $\mathbb{F}_qG$ can be deduced from the Wedderburn decomposition of $\mathbb{F}_q(G/H)$, where $H$ is a normal subgroup of $G$ having two elements and $q=p^k$ for some prime $p$ and $k\in \mathbb{Z}^+$.
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Key Findings & Data:In this paper, we derive a condition under which the Wedderburn decomposition of a semisimple group algebra $\mathbb{F}_qG$ can be deduced from the Wedderburn decomposition of $\mathbb{F}_q(G/H)$, where $H$ is a normal subgroup of $G$ having two elements and $q=p^k$ for some prime $p$ and $k\in \mathbb{Z}^+$.
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Conclusion & Impact:In order to complement the abstract theory of the paper, we deduce the Wedderburn decomposition and hence the unit group of semisimple group algebra $\mathbb{F}_q(A_5\rtimes C_4)$, where $A_5\rtimes C_4$ is a non-metabelian group and $C_4$ is a cyclic group of order $4$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Wedderburn decomposition · unit group · finite field
Abstract
In this paper, we derive a condition under which the Wedderburn decomposition of a semisimple group algebra $\mathbb{F}_qG$ can be deduced from the Wedderburn decomposition of $\mathbb{F}_q(G/H)$, where $H$ is a normal subgroup of $G$ having two elements and $q=p^k$ for some prime $p$ and $k\in \mathbb{Z}^+$. In order to complement the abstract theory of the paper, we deduce the Wedderburn decomposition and hence the unit group of semisimple group algebra $\mathbb{F}_q(A_5\rtimes C_4)$, where $A_5\rtimes C_4$ is a non-metabelian group and $C_4$ is a cyclic group of order $4$.
MITTAL, G., SHARMA, R. K. (2022). Wedderburn decomposition of a semisimple group algebra $\mathbb{F}_qG$ from a subalgebra of factor group of $G$. International Electronic Journal of Algebra, Cilt: 32 Sayı: 32, 91–100. https://ajindex.com/articles/918601
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