On generalized $\Pi$-property of subgroups of finite groups

Abstract

In this note, we extend the concept of $\Pi$-property of subgroups of finite groups and generalize some recent results. In particular, we generalize the main results of Li and Miao, p-Hypercyclically embedding and $\Pi$-property of subgroups of finite groups, Comm. Algebra 45 (2017), no. 8, pp. 3468–3474. and Miao, Ballester-Bolinches, Esteban-Romero, and Li, On the supersoluble hypercentre of a finite group, Monatsh. Math. 184 (2017), no. 4, pp. 641–648.