Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuG
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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.
2014 ◽
Vol 90
(2)
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pp. 220-226
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2008 ◽
Vol 01
(03)
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pp. 369-382
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1989 ◽
Vol 12
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pp. 263-266
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2021 ◽
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(2)
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pp. 147-156
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1997 ◽
Vol 40
(2)
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pp. 243-246
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