Sottogruppi massimali dei sottogruppi di Sylow e complementi normali
In this Note conditions for the existence of a normal -complement and for the supersolubility of a finite group are given.
In this Note conditions for the existence of a normal -complement and for the supersolubility of a finite group are given.
Let be a group and an integer . We say that has the -permutation property if, for any elements in , there exists some permutation of , such that . We prouve that every group is an FC-nilpotent group of class , and that a finitely generated group has the -permutation property (for some ) if, and only if, it is abelian by finite. We prouve also that a group if, and only if, its derived subgroup has order at most 2.
Groups all whose nonidentity subgroups split over a normal inseparable nonidentity subgroup are studied.
In this paper we study the class of finite groups whose nilpotent residual is a Hall subgroup having all subgroups normal in .