In this note, we extend the concept of Π-property of subgroups of finite groups and generalize some recent results. In particular, we generalize the main results of Li et al. [p-Hypercyclically embedding and Π-property of subgroups of finite groups, Comm. Algebra 45(8)(2017), 3468–3474] and Miao et al. [On the supersoluble hypercentre of a finite group, Monatsh. Math. (2016)]. Mathematics Subje...

Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $...

We demonstrate that two supersoluble complements of an abelian base in a finite split extension are conjugate if and only if, for each prime $p$, Sylow $p$-subgroup one complement is to the other. As corollary, we find any subgroup $N$ $G$ there exists $S$ such $S\cap N$ $G$. In particular, restricting groups allows us ease D. G. Higman's stipulation be within $S$. then consider group actions o...

Recall that a group is called semiabelian if it is generated by its normal cyclic subgroups [6]. The class of semiabelian groups is a very natural generalization of the wellknown class of Dedekind groups (the groups in which all cyclic subgroups are normal). In the paper [6] Venzke showed that these groups could play a major role in the theory of supersoluble finite groups. Based on the notion ...

We study finite groups in which every maximal subgroup is supersoluble or normal. Our results answer some questions arising from papers of Asaad and Rose.

‎in this paper we give a new condition for a sylow $p$-subgroup of a finite group to control transfer‎. ‎then it is deduced a characteri-zation of supersoluble groups that can be seen as a generalization of the well known result concerning the supersolubility of finite groups with cyclic sylow subgroups‎. moreover a condition for a normal embedding of a strongly closed $p$-subgroup is given‎. ...