a subgroup x of a group g is said to be an h -subgroup if n_g(x) ∩ x^g ≤ x for each element g belonging to g. in [m. bianchi e. a., on finite soluble groups in which normality is a transitive relation, j. group theory, 3 (2000), 147–156] the authors showed that finite groups in which every subgroup has the h -property are exactly soluble groups in which normality is a transitive relation. here ...

Abstract In this paper, we set ? ? ( G stretchy="false">) \eta(G) to be the number of conjugacy classes maximal cyclic subgroups a finite group ????. We compute for all metacyclic ????-groups. show that if ???? is ????-group order <m:msup...

We call a group $G$ belongs to the class of groups $S_{p}'$, if for every $pd$-chief factor $A/B$ $G$, $((A/B)_{p})'=1$. In this paper, we investigate influence some second maximal subgroups which are related non-$c_{p}$-normal on structure $S_{p}'$.