The influence of c-subnormality subgroups on the structure of finite groups

Let H be a subgroup of a group G. We say that H is c-subnormal in G if there exists a subnormal subgroup T of G such that H ⁢ T = G {HT=G} and H ∩ T ⩽ H G {H\cap T\leqslant H_{G}} , where H G {H_{G}} is the maximal normal subgroup of G which is contained in H. In this paper, we investigate the structure of a finite group G under the assumption that all maximal subgroups are c-subnormal subgroups and present some new conditions for supersolvability.