On m-Embedded Primary Subgroups of Finite Groups

Abstract

Suppose that A is a subgroup of a group G. A is called to be m-embedded in G if G has a subnormal subgroup T and a $\{1\le G\}$-embedded subgroup C such that $G=AT$ and $A\cap T\le C\le A$. In this paper, we shall investigate the structure of finite groups by using m-embedded subgroups and obtain some new characterization about p-supersolvability and generalized hypercentre of finite groups. Some results in Guo and Shum (Arch Math 80:561–569, 2003) , Ramadan et al. (Arch Math 85:203–210, 2005), Tang and Miao (Turk J Math 39:501–506, 2015), and Xu and Zhang (Can Math Bull 57(4):884–889, 2014) are generalized.

Keywords

m-Embedded subgroup / Sylow subgroup / p-Supersolvability / Generalized hypercentre

Funding

NSFC(11271016)

Qing Lan project of Jiangsu Province

High-level personnel of support program of Yangzhou University

333 high-level personnel training project in Jiangsu Province