Some results on the main supergraph of finite groups
Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x) | o(y) or o(y) | o(x). In this paper, we will show that G ≅ PSL(2, p) or PGL(2, p) if and only if S(G) ≅ S(PSL(2, p)) or S( PGL(2, p)), respectively. Also, we...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188561 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Some results on the main supergraph of finite groups / A.K. Asboei, S.S. Salehi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 172–178. — Бібліогр.: 17 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862688445386719232 |
|---|---|
| author | Asboei, A.K. Salehi, S.S. |
| author_facet | Asboei, A.K. Salehi, S.S. |
| citation_txt | Some results on the main supergraph of finite groups / A.K. Asboei, S.S. Salehi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 172–178. — Бібліогр.: 17 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x) | o(y) or o(y) | o(x). In this paper, we will show that G ≅ PSL(2, p) or PGL(2, p) if and only if S(G) ≅ S(PSL(2, p)) or S( PGL(2, p)), respectively. Also, we will show that if M is a sporadic simple group, then G ≅ M if only if S(G) ≅ S(M).
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| first_indexed | 2025-12-07T16:08:35Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188561 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:08:35Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Asboei, A.K. Salehi, S.S. 2023-03-06T14:22:13Z 2023-03-06T14:22:13Z 2020 Some results on the main supergraph of finite groups / A.K. Asboei, S.S. Salehi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 172–178. — Бібліогр.: 17 назв. — англ. 1726-3255 DOI:10.12958/adm584 2010 MSC: 20D08; 05C25. https://nasplib.isofts.kiev.ua/handle/123456789/188561 Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x) | o(y) or o(y) | o(x). In this paper, we will show that G ≅ PSL(2, p) or PGL(2, p) if and only if S(G) ≅ S(PSL(2, p)) or S( PGL(2, p)), respectively. Also, we will show that if M is a sporadic simple group, then G ≅ M if only if S(G) ≅ S(M). The authors would like to thank the referee for his/her careful reading and useful suggestions which led us to improve the paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Some results on the main supergraph of finite groups Article published earlier |
| spellingShingle | Some results on the main supergraph of finite groups Asboei, A.K. Salehi, S.S. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188561 |
| work_keys_str_mv | AT asboeiak someresultsonthemainsupergraphoffinitegroups AT salehiss someresultsonthemainsupergraphoffinitegroups |