Some results on the main supergraph of finite groups
Let \(G\) be a finite group. The main supergraph \(\mathcal{S}(G)\) is a graph with vertex set \(G\) in which two vertices \(x\) and \(y\) are adjacent if and only if \(o(x) \mid o(y)\) or \(o(y)\mid o(x)\). In this paper, we will show that \(G\cong \mathrm{PSL}(2,p)\) or \(\mathrm{PGL}(2,p)\) if an...
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| Datum: | 2021 |
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| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2021
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/584 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543064596676608 |
|---|---|
| author | Asboei, A. K. Salehi, S. S. |
| author_facet | Asboei, A. K. Salehi, S. S. |
| author_sort | Asboei, A. K. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-01-29T09:38:49Z |
| description | Let \(G\) be a finite group. The main supergraph \(\mathcal{S}(G)\) is a graph with vertex set \(G\) in which two vertices \(x\) and \(y\) are adjacent if and only if \(o(x) \mid o(y)\) or \(o(y)\mid o(x)\). In this paper, we will show that \(G\cong \mathrm{PSL}(2,p)\) or \(\mathrm{PGL}(2,p)\) if and only if \(\mathcal{S}(G)\cong \mathcal{S}(\mathrm{PSL}(2,p))\) or \(\mathcal{S}(\mathrm{PGL}(2,p))\), respectively. Also, we will show that if \(M\) is a sporadic simple group, then \(G\cong M\) if only if \(\mathcal{S}(G)\cong \mathcal{S}(M)\). |
| first_indexed | 2025-12-02T15:50:15Z |
| format | Article |
| id | admjournalluguniveduua-article-584 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:50:15Z |
| publishDate | 2021 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-5842021-01-29T09:38:49Z Some results on the main supergraph of finite groups Asboei, A. K. Salehi, S. S. graph, main supergraph, finite groups, Thompson's problem 20D08; 05C25 Let \(G\) be a finite group. The main supergraph \(\mathcal{S}(G)\) is a graph with vertex set \(G\) in which two vertices \(x\) and \(y\) are adjacent if and only if \(o(x) \mid o(y)\) or \(o(y)\mid o(x)\). In this paper, we will show that \(G\cong \mathrm{PSL}(2,p)\) or \(\mathrm{PGL}(2,p)\) if and only if \(\mathcal{S}(G)\cong \mathcal{S}(\mathrm{PSL}(2,p))\) or \(\mathcal{S}(\mathrm{PGL}(2,p))\), respectively. Also, we will show that if \(M\) is a sporadic simple group, then \(G\cong M\) if only if \(\mathcal{S}(G)\cong \mathcal{S}(M)\). Lugansk National Taras Shevchenko University 2021-01-29 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/584 10.12958/adm584 Algebra and Discrete Mathematics; Vol 30, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/584/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/584/794 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/584/812 Copyright (c) 2021 Algebra and Discrete Mathematics |
| spellingShingle | graph main supergraph finite groups Thompson's problem 20D08 05C25 Asboei, A. K. Salehi, S. S. Some results on the main supergraph of finite groups |
| title | Some results on the main supergraph of finite groups |
| title_full | Some results on the main supergraph of finite groups |
| title_fullStr | Some results on the main supergraph of finite groups |
| title_full_unstemmed | Some results on the main supergraph of finite groups |
| title_short | Some results on the main supergraph of finite groups |
| title_sort | some results on the main supergraph of finite groups |
| topic | graph main supergraph finite groups Thompson's problem 20D08 05C25 |
| topic_facet | graph main supergraph finite groups Thompson's problem 20D08 05C25 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/584 |
| work_keys_str_mv | AT asboeiak someresultsonthemainsupergraphoffinitegroups AT salehiss someresultsonthemainsupergraphoffinitegroups |