On $\mathfrak{F}_h $-normal subgroups of finite groups

Abstract

Let G be a finite group, and let $\mathfrak{F}$ be a formation of finite groups. We say that a subgroup H of G is $\mathfrak{F}_h $-normal in G if there exists a normal subgroup T of G such that HT is a normal Hall subgroup of G and (H ∩ T)H_G/H_G is contained in the $\mathfrak{F}$-hypercenter $Z_\infty ^\mathfrak{F} $ (G/H_G) of G/H_G. In this paper, we obtain some results about the $\mathfrak{F}_h $-normal subgroups and then use them to study the structure of finite groups.

Keywords

Finite group / $\mathfrak{F}_h$-normal subgroup / Sylow subgroup / maximal subgroup / 2-maximal subgroup

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