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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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}$.


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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