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Journals / Hacettepe Journal of Mathematics and Statistics / 2014 / Cilt: 43 - Sayı: 5

A new characterization of symmetric groups for some

Ali IRANMANESH
Alireza Khalili ASBOEİ
Seyed Sadegh Salehi AMİRİ
Pages
715–723
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

In this paper, we prove that if G is agroup such that nse(G)=nse(Sn) where n ∈ {3, 4, 5, 6, 7}, then G ∼= Sn.2000 AMS Classification: 20D60, 20D06

📌 3 Key Takeaways

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Objective & Hypothesis:Let G be a finite group and let πe(G) be the set of element orders G.Let k ∈ πe(G) and let mk be the number of elements of order k in G.Set nse(G):={mk|k ∈ πe(G)}.
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Key Findings & Data:Let G be a finite group and let πe(G) be the set of element orders G.Let k ∈ πe(G) and let mk be the number of elements of order k in G.Set nse(G):={mk|k ∈ πe(G)}.
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Conclusion & Impact:In this paper, we prove that if G is agroup such that nse(G)=nse(Sn) where n ∈ {3, 4, 5, 6, 7}, then G ∼= Sn.2000 AMS Classification: 20D60, 20D06
🔬Design:Research Article
📍Scope:2000 Verileri
⚙️Variables:Domain Parameters

Abstract

Let G be a finite group and let πe(G) be the set of element orders G.Let k ∈ πe(G) and let mk be the number of elements of order k in G.Set nse(G):={mk|k ∈ πe(G)}. In this paper, we prove that if G is agroup such that nse(G)=nse(Sn) where n ∈ {3, 4, 5, 6, 7}, then G ∼= Sn.2000 AMS Classification: 20D60, 20D06

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Cite This Article

IRANMANESH, A., ASBOEİ, A. K., AMİRİ, S. S. S. (2022). A new characterization of symmetric groups for some. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 5, 715–723. https://ajindex.com/articles/530345

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