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Journals / Journal of Algebra Combinatorics Discrete Structures and Applications / 2022 / Cilt: 9 Sayı: 2

On the isomorphism of unitary subgroups of noncommutative group algebras

Zsolt Adam Balogh(United Arab Emirates University)
Pages
45–51
Publication Date
2022-05-13
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AI Summary & Key Takeaways

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

In this paper we present a non-abelian p p -group G G whose group algebra F G FG has sharply less number of non-isomorphic * \cd -unitary subgroups than the given upper bound.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let F G FG be the group algebra of a finite p p -group G G over a field F F of characteristic p p .
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Key Findings & Data:Let * \cd be an involution of the group algebra F G FG which arises form the group basis G G .
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Conclusion & Impact:In this paper we present a non-abelian p p -group G G whose group algebra F G FG has sharply less number of non-isomorphic * \cd -unitary subgroups than the given upper bound.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Group ring · Group of units · Unitary subgroup

Abstract

Let F G FG be the group algebra of a finite p p -group G G over a field F F of characteristic p p . Let * \cd be an involution of the group algebra F G FG which arises form the group basis G G . The upper bound for the number of non-isomorphic * \cd -unitary subgroups is the number of conjugacy classes of the automorphism group G G with all the elements of order two. The upper bound is not always reached in the case when G G is an abelian group, but for non-abelian case the question is open. In this paper we present a non-abelian p p -group G G whose group algebra F G FG has sharply less number of non-isomorphic * \cd -unitary subgroups than the given upper bound.

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Cite This Article

Balogh, Z. A. (2022). On the isomorphism of unitary subgroups of noncommutative group algebras. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 9 Sayı: 2, 45–51. https://doi.org/10.13069/jacodesmath.1111746

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