Products of Sylow groups
type: Item
instance of: scholarly article
title: Products of Sylow groups
zbMATH Open document ID: 0811.20020
DOI: 10.1007/BF01189562
author: Michael B. Ward
author: Michael J. J. Barry
published in: Archiv der Mathematik
publication date: 1994-11-13T00:00:00Z
review text: The authors prove that a finite group \(G\) is solvable if and only if the product in any order of any representative set of Sylow subgroups of \(G\) equals \(G\), where a representative set of Sylow subgroups is one that contains exactly one Sylow \(p\)-subgroup for each prime \(p\) dividing the order of the group. That confirms a conjecture made (implicitly) by Philip Hall.
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 687020
zbMATH Keywords: finite solvable groups
zbMATH Keywords: product of Sylow subgroups
MaRDI profile type: Publication
cites work: A Characteristic Property of Soluble Groups
cites work: On products of Sylow subgroups in finite groups
cites work: Nonsolvable finite groups all of whose local subgroups are solvable
full work available at URL: https://doi.org/10.1007/bf01189562
OpenAlex ID: W2071256762
description: scientific article; zbMATH DE number 687020