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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 2

On generalized autocommutativity degree of finite groups

Parama Dutta0000-0002-6984-9817
Rajat Kanti Nath0000-0003-4766-6523
Pages
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Publication Date
2019-04-01
DOI
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AI Summary & Key Takeaways

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

In this paper we introduce and study the probability that the autocommutator of a randomly chosen pair of elements, one from $H$ and the other from Aut$(G)$ , is equal to a given element of $G$.

📌 3 Key Takeaways

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Objective & Hypothesis:Let $H$ be a subgroup of a finite group $G$ and Aut$(G)$ be the automorphism group of $G$.
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Key Findings & Data:Let $H$ be a subgroup of a finite group $G$ and Aut$(G)$ be the automorphism group of $G$.
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Conclusion & Impact:In this paper we introduce and study the probability that the autocommutator of a randomly chosen pair of elements, one from $H$ and the other from Aut$(G)$ , is equal to a given element of $G$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:automorphism group · autocommutativity degree · autoisoclinism

Abstract

Let $H$ be a subgroup of a finite group $G$ and Aut$(G)$ be the automorphism group of $G$. In this paper we introduce and study the probability that the autocommutator of a randomly chosen pair of elements, one from $H$ and the other from Aut$(G)$ , is equal to a given element of $G$.

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Cite This Article

Dutta, P., Nath, R. K. (2019). On generalized autocommutativity degree of finite groups. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 2. https://ajindex.com/articles/1402815

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