On $\mathcal {F}$-abnormal maximal subgroups of a finite solvable group
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- by Paul Venzke PDF
- Proc. Amer. Math. Soc. 33 (1972), 316-318 Request permission
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
- Roger Carter and Trevor Hawkes, The ${\cal F}$-normalizers of a finite soluble group, J. Algebra 5 (1967), 175–202. MR 206089, DOI 10.1016/0021-8693(67)90034-8
- Wolfgang Gaschütz, Über die $\Phi$-Untergruppe endlicher Gruppen, Math. Z. 58 (1953), 160–170 (German). MR 57873, DOI 10.1007/BF01174137
- Bertram Huppert, Zur Theorie der Formationen, Arch. Math. (Basel) 19 (1969), 561–574 (1969) (German). MR 244382, DOI 10.1007/BF01899382
Additional Information
- © Copyright 1972 American Mathematical Society
- 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