Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuG
Let G be a finite group and u be the class of all finite supersoluble groups. A supersoluble subgroup U of G is called u-maximal in G if for any supersoluble subgroup V of G containing U, V=U. Moreover, IntuG is the intersection of all u-maximal subgroups of G. This paper obtains some new criteria o...
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Wiley
2019-01-01
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| Series: | Journal of Chemistry |
| Online Access: | http://dx.doi.org/10.1155/2019/8517548 |
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| author | Li Zhang Zheng-Qun Cai |
| author_facet | Li Zhang Zheng-Qun Cai |
| author_sort | Li Zhang |
| collection | DOAJ |
| description | Let G be a finite group and u be the class of all finite supersoluble groups. A supersoluble subgroup U of G is called u-maximal in G if for any supersoluble subgroup V of G containing U, V=U. Moreover, IntuG is the intersection of all u-maximal subgroups of G. This paper obtains some new criteria on IntuG, by assuming that some subgroups of G are either Φ-I-supplemented or Φ-I-embedded in G. Here, a subgroup H of G is called Φ-I-supplemented in G if there exists a subnormal subgroup T of G such that G=HT and H∩THG/HG≤ΦH/HGIntuG and Φ-I-embedded in G if there exists a S-quasinormal subgroup T of G such that HT is S-quasinormal in G and H∩THG/HG≤ΦH/HGIntuG. |
| format | Article |
| id | doaj-art-2046a8eb6f144316887018689090ce70 |
| institution | Kabale University |
| issn | 2090-9063 2090-9071 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Chemistry |
| spelling | doaj-art-2046a8eb6f144316887018689090ce702025-02-03T01:28:52ZengWileyJournal of Chemistry2090-90632090-90712019-01-01201910.1155/2019/85175488517548Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuGLi Zhang0Zheng-Qun Cai1School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaSchool of Foreign Studies, Anhui Jianzhu University, Hefei 230601, ChinaLet G be a finite group and u be the class of all finite supersoluble groups. A supersoluble subgroup U of G is called u-maximal in G if for any supersoluble subgroup V of G containing U, V=U. Moreover, IntuG is the intersection of all u-maximal subgroups of G. This paper obtains some new criteria on IntuG, by assuming that some subgroups of G are either Φ-I-supplemented or Φ-I-embedded in G. Here, a subgroup H of G is called Φ-I-supplemented in G if there exists a subnormal subgroup T of G such that G=HT and H∩THG/HG≤ΦH/HGIntuG and Φ-I-embedded in G if there exists a S-quasinormal subgroup T of G such that HT is S-quasinormal in G and H∩THG/HG≤ΦH/HGIntuG.http://dx.doi.org/10.1155/2019/8517548 |
| spellingShingle | Li Zhang Zheng-Qun Cai Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuG Journal of Chemistry |
| title | Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuG |
| title_full | Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuG |
| title_fullStr | Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuG |
| title_full_unstemmed | Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuG |
| title_short | Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuG |
| title_sort | theoretical researches about u maximal subgroups and its applications in charactering intug |
| url | http://dx.doi.org/10.1155/2019/8517548 |
| work_keys_str_mv | AT lizhang theoreticalresearchesaboutumaximalsubgroupsanditsapplicationsincharacteringintug AT zhengquncai theoreticalresearchesaboutumaximalsubgroupsanditsapplicationsincharacteringintug |