\(p\)-supersolvability of factorized finite groups
type: Item
instance of: scholarly article
title: \(p\)-supersolvability of factorized finite groups
zbMATH Open document ID: 0804.20015
author: Angel Carocca
published in: Hokkaido Mathematical Journal
publication date: 1993-04-01T00:00:00Z
review text: The author calls two subgroups \(H\), \(K\) of a group mutually permutable if \(H\) is permutable with every subgroup of \(K\) and \(K\) is permutable with every subgroup of \(H\). He obtains the following main results: If \(G = HK \neq 1\) and \(H\) and \(K\) are mutually permutable, then \(H\) or \(K\) contains a nontrivial normal subgroup of \(G\) or \(F(G) \neq 1\) (Theorem A). If \(G = HK\) and \(H\) and \(K\) are \(p\)-supersoluble and mutually permutable, if further \(G'\) is \(p\)-nilpotent, then \(G\) is \(p\)-supersoluble (Theorem B). -- If \(G = HK\), where \(H\) and \(K\) are mutually permutable, \(H\) is \(p\)- supersoluble and \(K\) is \(p\)-nilpotent, then \(G\) is \(p\)-supersoluble.
reviewed by: Hermann Heineken
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 149282
zbMATH Keywords: mutually permutable subgroups
zbMATH Keywords: normal subgroup
zbMATH Keywords: \(p\)-supersoluble
zbMATH Keywords: \(p\)- nilpotent
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381413718
OpenAlex ID: W2092546820
DOI: 10.14492/HOKMJ/1381413718
description: scientific article; zbMATH DE number 149282