On generalized SΦ-supplemented subgroups of finite groups

According to Mao et al. (2016), let H be a subgroup of a finite group G; then H is said to be generalized S Phi-supplemented in G if there exists a subnormal subgroup T of G such that G = HT and (H boolean AND T) H-sG/H-sG <= Phi(H/H-sG), where H-sG is the subgroup of H generated by all those subgroups of H which are S-permutable in G. In this paper, we extend the concept of generalized S Phi-supplemented subgroups and generalize the main result of Mao et al. (2016).