On M-normal embedded subgroups and the structure of finite groups - Chen, Ruifang; Zhao, Xianhe; Li, Rui (MATHEMATICA SCANDINAVICA, 2021)
Let G be a group and H be a subgroup of G. H is said to be M-normal supplemented in G if there exists a normal subgroup K of G such that G=HK and H_1K<G for every maximal subgroup H_1 of H. Furthermore, H is said to be M-normal embedded in G if there exists a normal subgroup K of G such that G=HK and HK=1 or HK is M-normal supplemented in G. In this paper, some new criteria for a group to be nilpotent and p-supersolvable for some prime p are obtained.