A new characterization of alternating groups
Let \(G\) be a finite group and let \(\pi_{e}(G)\) be the set of element orders of \(G \). Let \(k \in \pi_{e}(G)\) and let \(m_{k}\) be the number of elements of order \(k \) in \(G\). Set nse(\(G\)):=\(\{ m_{k} | k \in \pi_{e}(G)\}\). In this paper, we show that if \(n = r\), \(r +1 \), \(r + 2\),...
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| Date: | 2018 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1042 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | Let \(G\) be a finite group and let \(\pi_{e}(G)\) be the set of element orders of \(G \). Let \(k \in \pi_{e}(G)\) and let \(m_{k}\) be the number of elements of order \(k \) in \(G\). Set nse(\(G\)):=\(\{ m_{k} | k \in \pi_{e}(G)\}\). In this paper, we show that if \(n = r\), \(r +1 \), \(r + 2\), \(r + 3\) \(r+4\), or \(r + 5\) where \(r\geq5\) is the greatest prime not exceeding \(n\), then \(A_{n}\) characterizable by nse and order. |
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