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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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1042 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543418180698112 |
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| author | Asboei, Alireza Khalili Amiri, Syyed Sadegh Salehi Iranmanesh, Ali |
| author_facet | Asboei, Alireza Khalili Amiri, Syyed Sadegh Salehi Iranmanesh, Ali |
| author_sort | Asboei, Alireza Khalili |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T02:28:53Z |
| description | 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. |
| first_indexed | 2025-12-02T15:41:44Z |
| format | Article |
| id | admjournalluguniveduua-article-1042 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:44Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-10422018-04-26T02:28:53Z A new characterization of alternating groups Asboei, Alireza Khalili Amiri, Syyed Sadegh Salehi Iranmanesh, Ali finite group, simple group, alternating groups 20D06, 20D60 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. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1042 Algebra and Discrete Mathematics; Vol 18, No 1 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1042/564 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | finite group simple group alternating groups 20D06 20D60 Asboei, Alireza Khalili Amiri, Syyed Sadegh Salehi Iranmanesh, Ali A new characterization of alternating groups |
| title | A new characterization of alternating groups |
| title_full | A new characterization of alternating groups |
| title_fullStr | A new characterization of alternating groups |
| title_full_unstemmed | A new characterization of alternating groups |
| title_short | A new characterization of alternating groups |
| title_sort | new characterization of alternating groups |
| topic | finite group simple group alternating groups 20D06 20D60 |
| topic_facet | finite group simple group alternating groups 20D06 20D60 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1042 |
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