On -quasinormal and -normal subgroups of a finite group
Let be a saturated formation containing the class of supersolvable groups and let be a finite group. The following theorems are presented: (1) if and only if there is a normal subgroup such that and every maximal subgroup of all Sylow subgroups of is either -normal or -quasinormally embedded in . (2) if and only if there is a normal subgroup such that and every maximal subgroup of all Sylow subgroups of , the generalized Fitting subgroup of , is either -normal or -quasinormally...