Finite Groups with Formation Subnormal Normalizers of Sylow Subgroups

A. F. Vasil'ev ; T. I. Vasilyeva ; A. G. Koranchuk

Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 679-691.

Résumé

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.

Détail

Keywords: finite group, Sylow subgroup, Sylow normalizer, $\mathfrak{F}$-subnormal subgroup, formation, hereditary saturated formation.

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