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On $ \mathcal{F}$-abnormal maximal subgroups of a finite solvable group


Author: Paul Venzke
Journal: Proc. Amer. Math. Soc. 33 (1972), 316-318
MSC: Primary 20D10
DOI: https://doi.org/10.1090/S0002-9939-1972-0291290-X
MathSciNet review: 0291290
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Abstract: Let $ \Delta (G)$ be the intersection of the nonnormal maximal subgroup of a finite group. W. Gaschütz has shown that $ \Delta (G)$ is nilpotent and that $ \Delta (G)/\Phi (G)$ is the center of $ G/\Phi (G)$. This note, by considering the intersection of the $ \mathfrak{F}$-abnormal maximal subgroups, generalizes these results for a saturated formation $ \mathfrak{F}$.


References [Enhancements On Off] (What's this?)

  • [1] Roger Carter and Trevor Hawkes, The $ \mathfrak{F}$-normalizers of a finite soluble group, J. Algebra 5 (1967), 175-202. MR 34 #5914. MR 0206089 (34:5914)
  • [2] Wolfgang Gaschütz, Über die $ \Phi $-Untergruppe endlicher Gruppen, Math. Z. 58 (1953), 160-170. MR 15, 285. MR 0057873 (15:285c)
  • [3] Bertram Huppert, Zur Theorie der Formationen, Arch. Math. (Basel) 19 (1968), 561-574. MR 39 #5697. MR 0244382 (39:5697)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291290-X
Keywords: Solvable group, formation, $ \mathfrak{F}$-abnormal, $ \mathfrak{F}$-hypercenter
Article copyright: © Copyright 1972 American Mathematical Society

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