Local c *-Supplementation of Some Subgroups in Finite Groups.

A subgroupHof a finite groupGis calledc*-supplemented inGif there exists a subgroupKofGsuch thatG = HKandH∩KisS-quasinormally embedded inG. In this paper, we investigate the localc*-supplementation of maximal subgroups of some Sylowp-subgroup and present some sufficient and necessary conditions for a finite group to bep-nilpotent. As applications, we give some sufficient conditions for a finite group to be in a saturated formation. [ABSTRACT FROM PUBLISHER]