A study on the structure of finite groups with \(c\)-subnormal subgroups
type: Item
instance of: scholarly article
title: A study on the structure of finite groups with \(c\)-subnormal subgroups
author: Jehad Jumah Al Jaraden
author: Dana J. Jaraden
published in: International Journal of Group Theory
publication date: 2024-10-11T00:00:00Z
review text: Let \(G\) be a finite group. A subgroup \(H \leq G\) is \(c\)-normal in \(G\) if there exists \(T \trianglelefteq G\) such that \(G=HT\) and \(T \cap H \leq H_{G}\), where \(H_{G}\) is the core of \(H\) in \(G\). Similarly, \(H\) is a \(c\)-subnormal subgroup in \(G\) if there exists a subnormal subgroup \(T\) of \(G\) such that \(G=HT\), and \(T \cap H \leq H_{G}\).\N\NThe purpose of the paper under review is to extend some known results on \(c\)-normal subgroups to \(c\)-subnormal subgroups. In particular, the authors prove two theorems that answer the question of what conditions \(c\)-subnormal subgroups must hold so that \(G\) is an element in a formation \(\mathfrak{U}\) of supersoluble groups (see Theorem 3.1 and Theorem 3.2).
reviewed by: Egle Bettio
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D35
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 7925507
zbMATH Keywords: saturated formation
zbMATH Keywords: \(c\)-subnormal subgroup
zbMATH Keywords: Sylow subgroup
zbMATH Keywords: supersoluble group
zbMATH Keywords: formation
MaRDI profile type: Publication
cites work: Influence of normality on maximal subgroups of Sylow subgroups of a finite group
DOI: 10.22108/IJGT.2023.137024.1847
description: scientific article; zbMATH DE number 7925507