On the intersection of a class of maximal subgroups of a finite group

Author:
Xiu Yun Guo

Journal:
Proc. Amer. Math. Soc. **106** (1989), 329-332

MSC:
Primary 20D20

DOI:
https://doi.org/10.1090/S0002-9939-1989-0999757-6

MathSciNet review:
999757

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Abstract: Let be a finite group and a set of primes. We consider the family of subgroups of is composite} and denote if is non-empty, otherwise . The purpose of this note is to prove

**Theorem**. *Let* *be a* *-solvable group. Then* *has the following properties*: (1) is supersolvable. (2) . (3) *is supersolvable if and only if* .

**[1]**W. E. Deskins,*On maximal subgroups*, First Sympos. Pure Math., Amer. Math. Soc. Providence, RI, 1959. MR**0125157 (23:A2462)****[2]**W. Gaschütz,*Über die Untergruppe endlicher Gruppen*, Math. Z.**58**(1953), 260-270. MR**0057873 (15:285c)****[3]**J. Rose,*The influence on a group of its abnormal structure*, J. Math. Lond. Soc.**40**(1965), 348-361. MR**0174638 (30:4838)****[4]**P. Bhattacharya and N. P. Mukherjee,*On the intersection of a class of maximal subgroups of a finite group*II, J. Pure and Applied Algebra (North-Holland)**42**(1986), 117-124. MR**857561 (88h:20028)****[5]**M. Weistein,*Between nilpotent and solvable*, Polygonal Publishing House, 1982. MR**655785 (84k:20002)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0999757-6

Keywords:
Finite group,
maximal subgroup

Article copyright:
© Copyright 1989
American Mathematical Society