EUDML

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On cover-avoiding subgroups of Sylow subgroups of finite groups

Yangming Li — 2010

Rendiconti del Seminario Matematico della Università di Padova

On $S$ -quasinormal and $c$ -normal subgroups of a finite group

Shirong Li; Yangming Li — 2008

Czechoslovak Mathematical Journal

Let $ℱ$ be a saturated formation containing the class of supersolvable groups and let $G$ be a finite group. The following theorems are presented: (1) $G \in ℱ$ if and only if there is a normal subgroup $H$ such that $G / H \in ℱ$ and every maximal subgroup of all Sylow subgroups of $H$ is either $c$ -normal or $S$ -quasinormally embedded in $G$ . (2) $G \in ℱ$ if and only if there is a normal subgroup $H$ such that $G / H \in ℱ$ and every maximal subgroup of all Sylow subgroups of $F^{*} (H)$ , the generalized Fitting subgroup of $H$ , is either $c$ -normal or $S$ -quasinormally...