SE-supplemented subgroups of finite groups
A Fitting set is called elementary if it consists of the subnormal subgroups of the conjugates of a given subgroup. In this paper we analyse the structure of the finite solvable groups in which every Fitting set is the insiemistic union of elementary Fitting sets whose intersection is the subgroup 1.
In this paper we study finite non abelian groups in which every proper normal subgroup and every proper epimorphic image is abelian. Also we study finite non nilpotent groups in which every normal subgroup and every proper epimorphic image is nilpotent and those finite soluble non nilpotent groups in which every proper normal subgroup is nilpotent.
In questa nota si studiano i gruppi finiti non supersolubili che hanno un solo sottogruppo normale massimale, e per cui ogni sottogruppo normale proprio e ogni immagine epimorfica propria è supersolubile.
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 .
The purpose of this paper is to study the subgroup embedding properties of S-semipermutability, semipermutability, and seminormality. Here we say H is S-semipermutable (resp. semipermutable) in a group Gif H permutes which each Sylow subgroup (resp. subgroup) of G whose order is relatively prime to that of H. We say H is seminormal in a group G if H is normalized by subgroups of G whose order is relatively prime to that of H. In particular, we establish that a seminormal p-subgroup is subnormal....
In this paper we study finite non abelian solvable groups in which every proper normal subgroup is abelian, and non-solvable ones in which every proper normal subgroup is abelian and has a basis of at most two elements.
We prove that every abelian finite group is contained in the intersection of the nontrivial normal classes introduced by Zappa.