Geodesic
Finite Groups with Formation Subnormal Normalizers of Sylow Subgroups
Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 679-691

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Let $\mathfrak{F}$ be a formation. Properties of the class $\mathrm{w}^{*}\mathfrak{F}$ of all groups $G$ for which $\pi(G)\subseteq\pi(\mathfrak{F})$ and the normalizers of all Sylow subgroups are $\mathfrak{F}$-subnormal in $G$ are studied. In particular, it is established that this class is a formation closed with respect to taking Hall subgroups. Hereditary saturated formations $\mathfrak{F}$ coinciding with $\mathrm{w}^{*}\mathfrak{F}$ are found.
Keywords: finite group, Sylow subgroup, Sylow normalizer, $\mathfrak{F}$-subnormal subgroup, formation, hereditary saturated formation. 
@article{MZM_2020_108_5_a3,
     author = {A. F. Vasil'ev and T. I. Vasilyeva and A. G. Koranchuk},
     title = {Finite {Groups} with {Formation} {Subnormal} {Normalizers} of {Sylow} {Subgroups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {679--691},
     publisher = {mathdoc},
     volume = {108},
     number = {5},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_5_a3/}
}
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A. F. Vasil'ev; T. I. Vasilyeva; A. G. Koranchuk. Finite Groups with Formation Subnormal Normalizers of Sylow Subgroups. Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 679-691. http://geodesic.mathdoc.fr/item/MZM_2020_108_5_a3/