Finite groups in which primary subgroups have cyclic cofactors.
type: Item
instance of: scholarly article
title: Finite groups in which primary subgroups have cyclic cofactors.
zbMATH Open document ID: 1236.20016
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2011-05-23T00:00:00Z
full work available at URL: vol34 2 13.html
review text: The authors prove the following theorem: Let \(G\) be a finite group, \(q\) be the largest prime divisor of \(|G|\) and \(\pi=\pi(G)\setminus\{q\}\). Suppose that the factor group \(X/\text{core}_GX\) is cyclic for every \(p\)-subgroup \(X\) of \(G\) and every \(p\in\pi\). Then: (1) \(G\) is solvable and its Hall \(\{2,3\}'\)-subgroup is normal in \(G\) and is a dispersive group of Ore; (2) All Hall \(\{2,3\}\)-subgroups of \(G\) are meta-nilpotent; (3) Every Hall \(p'\)-subgroup of \(G\) is a dispersive group of Ore, for every \(p\in\{2,3\}\); (4) \(l_r(G)\leq 1\), for all \(r\in\pi(G)\).
reviewed by: Rodica Covaci
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 5899045
zbMATH Keywords: finite groups
zbMATH Keywords: cofactors of subgroups
zbMATH Keywords: \(p\)-lengths
zbMATH Keywords: dispersive groups
author: Yufeng Liu
author: Xiaolan Yi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5899045