The finite groups with no real \(p\)-elements.
type: Item
instance of: scholarly article
title: The finite groups with no real \(p\)-elements.
zbMATH Open document ID: 1269.20016
author: Silvio Dolfi
author: Gunter Malle
author: Gabriel Navarro
published in: Israel Journal of Mathematics
publication date: 2013-02-07T00:00:00Z
review text: The authors use the classification of finite simple groups to investigate finite groups satisfying the condition of the title, where \(p\) is an odd prime. They look in detail at the case when \(G\) is a simple group, providing a specific list of groups in this case. They use this to obtain also more general results. They prove that if \(G\) is a finite group with no non-trivial quotients of odd order, \(p\) is any odd prime dividing the order of \(G\) and \(G\) has no real elements of order \(p\), then \(G\) is not \(p\)-solvable and \(G\) has Abelian Sylow \(p\)-subgroups. In addition, the special cases when \(p=3\) and \(p=5\) are treated in more detail.
reviewed by: Alexandre Turull
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 6135119
zbMATH Keywords: classification of finite groups
zbMATH Keywords: real elements
zbMATH Keywords: \(p\)-elements
zbMATH Keywords: Abelian Sylow subgroups
MaRDI profile type: Publication
full work available at URL: s11856-012-0054-8
OpenAlex ID: W1973407264
cites work: Q3684278
cites work: Q4375273
cites work: Q3077960
cites work: Real characters and degrees.
DOI: 10.1007/S11856-012-0054-8
description: scientific article; zbMATH DE number 6135119