SΦ-Supplemented subgroups of finite groups - Li, Xianhua; Zhao, Tao (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We call H an SΦ-supplemented subgroup of a finite group G if there exists a subnormal subgroup T of G such that G = HT and H T ≤ Φ(H), where Φ(Н) is the Frattini subgroup of H. In this paper, we characterize the p-nilpotency and supersolubility of a finite group G under the assumption that every subgroup of a Sylow p-subgroup of G with given order is SΦ-supplemented in G. Some results about formations are also obtained.