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Journals / Hacettepe Journal of Mathematics and Statistics / 2017 / Cilt: 46 - Sayı: 2

Centralizers and the maximum size of the pairwise noncommuting elements in finite groups

Seyyed Majid Jafarian AMİRİ
Hojjat ROSTAMİ
Pages
193–198
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

As an application of this result, we obtain the sharp lower bound for $\omega(G)$ in terms of the order of $G$ where $\omega(G)$ is the maximum size of a set of the pairwise noncommuting elements of $G$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, we determine the structure of all nonabelian groups $G$ such that $G$ has the minimum number of the element centralizers amongnonabelian groups of the same order.
📊
Key Findings & Data:In this article, we determine the structure of all nonabelian groups $G$ such that $G$ has the minimum number of the element centralizers amongnonabelian groups of the same order.
💡
Conclusion & Impact:As an application of this result, we obtain the sharp lower bound for $\omega(G)$ in terms of the order of $G$ where $\omega(G)$ is the maximum size of a set of the pairwise noncommuting elements of $G$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:finite group · centralizer · CA-group

Abstract

In this article, we determine the structure of all nonabelian groups $G$ such that $G$ has the minimum number of the element centralizers amongnonabelian groups of the same order. As an application of this result, we obtain the sharp lower bound for $\omega(G)$ in terms of the order of $G$ where $\omega(G)$ is the maximum size of a set of the pairwise noncommuting elements of $G$.

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Cite This Article

AMİRİ, S. M. J., ROSTAMİ, H. (2022). Centralizers and the maximum size of the pairwise noncommuting elements in finite groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 2, 193–198. https://ajindex.com/articles/529998

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