A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group
Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K≤M and G=MH, we called the order of H/K the normal index of M and M∩H/K a section of M in G. Using the concepts of normal index and c-section, we obtain some new characterizations of p-solvable, 2-supersolvable,...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/921804 |
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| _version_ | 1832561707396890624 |
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| author | Na Tang Xianhua Li |
| author_facet | Na Tang Xianhua Li |
| author_sort | Na Tang |
| collection | DOAJ |
| description | Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K≤M and G=MH, we called the order of H/K the normal index of M and M∩H/K a section of M in G. Using the concepts of normal index and c-section, we obtain some new characterizations of p-solvable, 2-supersolvable, and p-nilpotent. |
| format | Article |
| id | doaj-art-60a09888ac4f45f5ab8723afa81a4af2 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-60a09888ac4f45f5ab8723afa81a4af22025-02-03T01:24:26ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/921804921804A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite GroupNa Tang0Xianhua Li1School of Mathematical Science, Soochow University, Suzhou 215006, ChinaSchool of Mathematical Science, Soochow University, Suzhou 215006, ChinaLet M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K≤M and G=MH, we called the order of H/K the normal index of M and M∩H/K a section of M in G. Using the concepts of normal index and c-section, we obtain some new characterizations of p-solvable, 2-supersolvable, and p-nilpotent.http://dx.doi.org/10.1155/2014/921804 |
| spellingShingle | Na Tang Xianhua Li A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group Journal of Applied Mathematics |
| title | A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group |
| title_full | A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group |
| title_fullStr | A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group |
| title_full_unstemmed | A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group |
| title_short | A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group |
| title_sort | note on the normal index and the c section of maximal subgroups of a finite group |
| url | http://dx.doi.org/10.1155/2014/921804 |
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