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Journals / International Electronic Journal of Algebra / 2026 / Volume: 29 Issue: 29

ON UNITARY SUBGROUPS OF GROUP ALGEBRAS

Zsolt Adam Balogh(United Arab Emirates University)
Pages
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Publication Date
2021-01-05
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AI Summary & Key Takeaways

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

A variant of the modular isomorphism question of group algebras is also considered.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$ and let $*$ be the classical involution of $FG$.
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Key Findings & Data:The $*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of all normalized units $u$ satisfying the property $u^*=u^{-1}$.
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Conclusion & Impact:A variant of the modular isomorphism question of group algebras is also considered.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Group ring · group of units · unitary subgroup

Abstract

Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$ and let $*$ be the classical involution of $FG$. The $*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of all normalized units $u$ satisfying the property $u^*=u^{-1}$. In this paper we give a recursive method how to compute the order of the $*$-unitary subgroup for certain non-commutative group algebras. A variant of the modular isomorphism question of group algebras is also considered.

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Cite This Article

Balogh, Z. A. (2021). ON UNITARY SUBGROUPS OF GROUP ALGEBRAS. International Electronic Journal of Algebra, Volume: 29 Issue: 29. https://doi.org/10.24330/ieja.852199

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