On the \(\mathcal{F}^*\)-norm of a finite group
type: Item
instance of: scholarly article
title: On the \(\mathcal{F}^*\)-norm of a finite group
DOI: 10.4171/RSMUP/77
author: Quanfu Yan
author: Zhencai Shen
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2021-07-02T00:00:00Z
review text: Summary: Let \(G\) be a finite group and \(\mathcal{F}\) be a non-empty formation. We define the \(\mathcal{F}^*\)-norm, denoted by \(N_{\mathcal{F}}^*(G)\), to be intersection of the normalizers of the \(\mathcal{F}\)-residuals of all \(F\)-subgroups of \(G\), where \(F=\mathcal{NF}\) is the class of all groups whose \(\mathcal{F}\)-residuals are nilpotent. In this paper, we research the properties of \(N_{\mathcal{F}}^*(G)\) and investigate the relationship between \(N_{\mathcal{F}}^*(G)\) and \(N_{\mathcal{F}}(G)\), where \(N_{\mathcal{F}}(G)\) is the intersection of the normalizers of the \(\mathcal{F}\)-residuals of all subgroups of \(G\). We show that \(N_{\mathcal{F}}^*(G)=N_{\mathcal{F}}(G)\) if \(\mathcal{A}\subseteq \mathcal{F}\subseteq\mathcal{N}\).
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 7367436
zbMATH Keywords: \(\mathcal{F}\)-residual
zbMATH Keywords: formation
zbMATH Keywords: \(F\)-subgroup
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/rsmup/77
OpenAlex ID: W3158185582
description: scientific article; zbMATH DE number 7367436