On a Maximal Subgroup 2^6:(3^. S6) of M24
The Mathieu group M24 has a maximal subgroup of the form G ̅=N:G, where N=26 and G=3. S6 ≅ 3. PGL2 (9). Using Atlas, we can see that M24 has only one maximal subgroup of type 26:(3. S6). The group is a split extension of an elementary abelian group, N=26 by a non-split extensionmgroup, G=3. S6. The...
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| Format: | Article |
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University of Kashan
2022-09-01
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| Series: | Mathematics Interdisciplinary Research |
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| Online Access: | https://mir.kashanu.ac.ir/article_112777_4e1f0384dc40e18b6b1c38cce416a193.pdf |
| _version_ | 1797630850332884992 |
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| author | Dennis Chikopela Thekiso Seretlo |
| author_facet | Dennis Chikopela Thekiso Seretlo |
| author_sort | Dennis Chikopela |
| collection | DOAJ |
| description | The Mathieu group M24 has a maximal subgroup of the form G ̅=N:G, where N=26 and G=3. S6 ≅ 3. PGL2 (9). Using Atlas, we can see that M24 has only one maximal subgroup of type 26:(3. S6). The group is a split extension of an elementary abelian group, N=26 by a non-split extensionmgroup, G=3. S6. The Fischer matrices for each class representative of G are computed which together with character tables of inertia factor groups of G lead to the full character table of G ̅. The complete fusion of G ̅ into the parent group M24 has been determined using the technique of set intersections of characters. |
| first_indexed | 2024-03-11T11:13:46Z |
| format | Article |
| id | doaj.art-b6cffd5fc0a04cfb94dcd612861fbc0b |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:13:46Z |
| publishDate | 2022-09-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-b6cffd5fc0a04cfb94dcd612861fbc0b2023-11-11T10:06:10ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652022-09-017319721610.22052/mir.2022.243014.1300112777On a Maximal Subgroup 2^6:(3^. S6) of M24Dennis Chikopela0Thekiso Seretlo1Department of Mathematics, The Copperbelt University, Kitwe Campus, ZambiaDepartment of Mathematical and Computer Sciences, University of Limpopo, Polokwane, South AfricaThe Mathieu group M24 has a maximal subgroup of the form G ̅=N:G, where N=26 and G=3. S6 ≅ 3. PGL2 (9). Using Atlas, we can see that M24 has only one maximal subgroup of type 26:(3. S6). The group is a split extension of an elementary abelian group, N=26 by a non-split extensionmgroup, G=3. S6. The Fischer matrices for each class representative of G are computed which together with character tables of inertia factor groups of G lead to the full character table of G ̅. The complete fusion of G ̅ into the parent group M24 has been determined using the technique of set intersections of characters.https://mir.kashanu.ac.ir/article_112777_4e1f0384dc40e18b6b1c38cce416a193.pdfmathieu groupconjugacy classesirreducible charactersfischer matricesfusions |
| spellingShingle | Dennis Chikopela Thekiso Seretlo On a Maximal Subgroup 2^6:(3^. S6) of M24 Mathematics Interdisciplinary Research mathieu group conjugacy classes irreducible characters fischer matrices fusions |
| title | On a Maximal Subgroup 2^6:(3^. S6) of M24 |
| title_full | On a Maximal Subgroup 2^6:(3^. S6) of M24 |
| title_fullStr | On a Maximal Subgroup 2^6:(3^. S6) of M24 |
| title_full_unstemmed | On a Maximal Subgroup 2^6:(3^. S6) of M24 |
| title_short | On a Maximal Subgroup 2^6:(3^. S6) of M24 |
| title_sort | on a maximal subgroup 2 6 3 s6 of m24 |
| topic | mathieu group conjugacy classes irreducible characters fischer matrices fusions |
| url | https://mir.kashanu.ac.ir/article_112777_4e1f0384dc40e18b6b1c38cce416a193.pdf |
| work_keys_str_mv | AT dennischikopela onamaximalsubgroup263s6ofm24 AT thekisoseretlo onamaximalsubgroup263s6ofm24 |