Groups with the same orders of Sylow normalizers as the Mathieu groups
There exist many characterizations for the sporadic simple groups. In this paper we give two new characterizations for the Mathieu sporadic groups. Let M be a Mathieu group and let p be the greatest prime divisor of |M|. In this paper, we prove that M is uniquely determined by |M| and |NM(P)|, where...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1449 |
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| author | Behrooz Khosravi Behnam Khosravi |
| author_facet | Behrooz Khosravi Behnam Khosravi |
| author_sort | Behrooz Khosravi |
| collection | DOAJ |
| description | There exist many characterizations for the sporadic simple groups.
In this paper we give two new characterizations for the Mathieu
sporadic groups. Let M be a Mathieu group and let p be the
greatest prime divisor of |M|. In this paper, we prove that M is uniquely determined by |M| and |NM(P)|, where P∈Sylp(M). Also we prove that if G is a finite group, then
G≅M if and only if for every prime q, |NM(Q)|=|NG(Q′)|, where Q∈Sylq(M) and Q′∈Sylq(G). |
| format | Article |
| id | doaj-art-1585a695a83a41a996a62a886eaaabbb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1585a695a83a41a996a62a886eaaabbb2025-02-03T06:00:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-01200591449145310.1155/IJMMS.2005.1449Groups with the same orders of Sylow normalizers as the Mathieu groupsBehrooz Khosravi0Behnam Khosravi1Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran 15914, IranDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran 19838, IranThere exist many characterizations for the sporadic simple groups. In this paper we give two new characterizations for the Mathieu sporadic groups. Let M be a Mathieu group and let p be the greatest prime divisor of |M|. In this paper, we prove that M is uniquely determined by |M| and |NM(P)|, where P∈Sylp(M). Also we prove that if G is a finite group, then G≅M if and only if for every prime q, |NM(Q)|=|NG(Q′)|, where Q∈Sylq(M) and Q′∈Sylq(G).http://dx.doi.org/10.1155/IJMMS.2005.1449 |
| spellingShingle | Behrooz Khosravi Behnam Khosravi Groups with the same orders of Sylow normalizers as the Mathieu groups International Journal of Mathematics and Mathematical Sciences |
| title | Groups with the same orders of Sylow normalizers as the Mathieu groups |
| title_full | Groups with the same orders of Sylow normalizers as the Mathieu groups |
| title_fullStr | Groups with the same orders of Sylow normalizers as the Mathieu groups |
| title_full_unstemmed | Groups with the same orders of Sylow normalizers as the Mathieu groups |
| title_short | Groups with the same orders of Sylow normalizers as the Mathieu groups |
| title_sort | groups with the same orders of sylow normalizers as the mathieu groups |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1449 |
| work_keys_str_mv | AT behroozkhosravi groupswiththesameordersofsylownormalizersasthemathieugroups AT behnamkhosravi groupswiththesameordersofsylownormalizersasthemathieugroups |