Research ArticleNo Access

On the generalized norms of finite groups

Lü Gong

School of Sciences, Nantong University, Jiangsu 226019, P. R. China

E-mail Address: lieningzai1917@126.com

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Tong Jiang

School of Sciences, Nantong University, Jiangsu 226019, P. R. China

E-mail Address: 530387858@qq.com

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, and

Baojun Li

School of Sciences, Nantong University, Jiangsu 226019, P. R. China

E-mail Address: libj@ntu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0219498822501213Cited by:2 (Source: Crossref)

Abstract

The norm $N (G)$ $N (G)$ of a group $G$ $G$ is the intersection of the normalizers of all subgroups in $G$ $G$ . In this paper, the norm is generalized by studying on Sylow subgroups and $ℋ$ -subgroups in finite groups which is denoted by $C (G)$ and $A (G)$ , respectively. It is proved that the generalized norms $A (G)$ and $C (G)$ are all equal to the hypercenter of $G$ .

Communicated by M. L. Lewis

Keywords:

AMSC: 20D10, 20D20

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