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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2090-9063 2090-9071 |