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Journals / Turkish Journal of Mathematics / 2022 / Cilt: 46 - Sayı: 3

Non-solvable groups all of whose indices are odd-square-free

Roghayeh HAFEZIEH BALAMAN
Sajjad MAHMOOD ROBATI
Pages
746–752
Publication Date
2022-11-01
DOI
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AI Summary & Key Takeaways

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

In this paper, we show that if G is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of G, which is an answer to the dual of the question mentioned by Huppert in [5].

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Given a finite group G and x ∈ G, the class size of x in G is called odd-square-free if it is not divisible by the square of any odd prime number.
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Key Findings & Data:Given a finite group G and x ∈ G, the class size of x in G is called odd-square-free if it is not divisible by the square of any odd prime number.
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Conclusion & Impact:In this paper, we show that if G is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of G, which is an answer to the dual of the question mentioned by Huppert in [5].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Given a finite group G and x ∈ G, the class size of x in G is called odd-square-free if it is not divisible by the square of any odd prime number. In this paper, we show that if G is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of G, which is an answer to the dual of the question mentioned by Huppert in [5].

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Cite This Article

BALAMAN, R. H., ROBATI, S. M. (2022). Non-solvable groups all of whose indices are odd-square-free. Turkish Journal of Mathematics, Cilt: 46 - Sayı: 3, 746–752. https://ajindex.com/articles/607283

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References (8)

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