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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
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 Maddede Bu Makale
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Amaç & Hipotez:Let G be a finite group and let πe(G) be the set of element orders G.
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Temel Bulgular & Veri:Let k ∈ πe(G) and let mk be the number of elements of order k in G.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap
Asboei, A. K., Amiri, S. S. S., Iranmanesh, A. (2014). A new characterization of symmetric groups for some n. Hacettepe Journal of Mathematics and Statistics, Volume: 43 Issue: 5. https://ajindex.com/articles/1403362