Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is odd
Let $G$ be a finite group and let $\Gamma(G) $ be the prime graph of $ G$. We assume that $ n\geq 17$ is an odd number. In this paper, we show that if $ \Gamma(G) = \Gamma(C_{n}(4))$, then $ G$ has a unique non-abelian composition factor isomorphic to $C_{n}(4)$. As consequences of our result, $C_{n...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2015-02-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/21969 |
| _version_ | 1818163685866078208 |
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| author | Somayeh Mosavi Neda Ahanjideh |
| author_facet | Somayeh Mosavi Neda Ahanjideh |
| author_sort | Somayeh Mosavi |
| collection | DOAJ |
| description | Let $G$ be a finite group and let $\Gamma(G) $ be the prime graph of $ G$. We assume that $ n\geq 17$ is an odd number. In this paper, we show that if $ \Gamma(G) = \Gamma(C_{n}(4))$, then $ G$ has a unique non-abelian composition factor isomorphic to $C_{n}(4)$. As consequences of our result, $C_{n}(4)$ is quasirecognizable by its spectrum and by prime graph. |
| first_indexed | 2024-12-11T16:53:30Z |
| format | Article |
| id | doaj.art-50938bf1869944ab9cc441d408d8c66f |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-11T16:53:30Z |
| publishDate | 2015-02-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-50938bf1869944ab9cc441d408d8c66f2022-12-22T00:58:03ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882015-02-01331576510.5269/bspm.v33i1.2196910705Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is oddSomayeh Mosavi0Neda Ahanjideh1Sahrekord University Department of pure Mathematics Faculty of Mathematical SciencesSahrekord University Department of pure Mathematics Faculty of Mathematical SciencesLet $G$ be a finite group and let $\Gamma(G) $ be the prime graph of $ G$. We assume that $ n\geq 17$ is an odd number. In this paper, we show that if $ \Gamma(G) = \Gamma(C_{n}(4))$, then $ G$ has a unique non-abelian composition factor isomorphic to $C_{n}(4)$. As consequences of our result, $C_{n}(4)$ is quasirecognizable by its spectrum and by prime graph.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/21969Quasirecognitionprime graphsimple groupelement order |
| spellingShingle | Somayeh Mosavi Neda Ahanjideh Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is odd Boletim da Sociedade Paranaense de Matemática Quasirecognition prime graph simple group element order |
| title | Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is odd |
| title_full | Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is odd |
| title_fullStr | Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is odd |
| title_full_unstemmed | Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is odd |
| title_short | Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is odd |
| title_sort | quasirecognition by prime graph of c n 4 where n geq17 is odd |
| topic | Quasirecognition prime graph simple group element order |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/21969 |
| work_keys_str_mv | AT somayehmosavi quasirecognitionbyprimegraphofcn4wherengeq17isodd AT nedaahanjideh quasirecognitionbyprimegraphofcn4wherengeq17isodd |