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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 a group such that nse(G)=nse(Sn) where n ∈ {3, 4, 5, 6, 7}, then G ∼= Sn.
📌 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.
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Key Findings & Data:Let k ∈ πe(G) and let mk be the number of elements of order k in G.
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Conclusion & Impact:In this paper, we prove that if G is a group such that nse(G)=nse(Sn) where n ∈ {3, 4, 5, 6, 7}, then G ∼= Sn.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Symmetric group · element order · set of the numbers of elements of the same order
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 a group such that nse(G)=nse(Sn) where n ∈ {3, 4, 5, 6, 7}, then G ∼= Sn.
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Cite This Article
ASBOEİ, A. K., AMİRİ, S. S. S., IRANMANESH, A. (2014). A new characterization of symmetric groups for some n. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 5, 715–723. https://ajindex.com/articles/669544