Properties Of Maximal Subgroups And Supersolvability Of Groups

There has been a fair amount of interest on the internal structure of groups. Let E be a characteristic of groups. A group is called an inner-Σ group, if all of its proper subgroups are E groups, but the group itself is a non-E group. There are a lot of results about inner-Σ groups. We study a generalized inner-Σ group (i.e.. some of its maximal subgroups are non-E groups, but any subgroup not included in these maximal subgroups possesses Σ). We consider the properties of maximal subgroups and super-solvability of groups, and obtain some characteristics of Σ groups, where E means p-closed or super-solvable.