Affiliation:
1. School of Mathematics, Jilin University, Changchun 130012, P. R. China
Abstract
In this paper, we introduce the concept of weakly [Formula: see text]-hypercyclically embedded subgroups, and investigate the influence of [Formula: see text]-supplemented subgroups on the structure of chief factors of finite groups. First, we find a connection between [Formula: see text]-supplemented subgroups and normally embedded subgroups. With the help of this connection, we give some criteria for (weakly) [Formula: see text]-hypercyclically embeddability of normal subgroups of finite groups by using fewer [Formula: see text]-supplemented [Formula: see text]-subgroups with given order. In particular, we not only simplify, but also improve the Main Theorem of [L. Miao and J. Zhang, On a class of non-solvable groups, J. Algebra 496 (2018) 1–10]. Finally, we point out that for a [Formula: see text]-subgroup [Formula: see text] of [Formula: see text], the concept of [Formula: see text]-embedded subgroups coincides with the concept of [Formula: see text]-supplemented subgroups.
Funder
China Postdoctoral Science Foundation
The Science and Technology Department Project of Jilin Province
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory