The \(P!\)-theorem
type: Item
instance of: scholarly article
title: The \(P!\)-theorem
zbMATH Open document ID: 1029.20011
DOI: 10.1016/S0021-8693(03)00075-9
author: Chris Parker
author: Gemma Parmeggiani
author: B. Stellmacher
published in: Journal of Algebra
publication date: 2003-06-09T00:00:00Z
review text: Recall that a group \(H\) is of characteristic \(p\) if \(C_H(O_p(H))\leq O_p(H)\) and is of local characteristic \(p\) if every \(p\)-local subgroup has characteristic \(p\). This paper is part of the project initiated by Meierfrankenfeld to classify all finite groups of local characteristic \(p\) that do not have a strongly embedded \(p\)-group. This is part of a proposed third generation proof of the classification of finite simple groups (and so of course one is not allowed to use the classification -- on the other hand, by assuming that the group is a minimal counterexample to the classification, one can assume that all proper sections of the group involve only the known simple groups). This is a difficult and deep paper and relies heavily on the amalgam method. The results and hypotheses are too technical to describe here. We refer the reader to the article and the references quoted there.
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 1924680
zbMATH Keywords: finite simple groups
zbMATH Keywords: local characteristic \(p\)
zbMATH Keywords: \(p\)-local subgroups
zbMATH Keywords: strongly embedded subgroups
reviewed by: Robert Guralnick
MaRDI profile type: Publication
cites work: Q3681018
cites work: Classification of \(2F\)-modules. I
cites work: Q4660830
cites work: Endliche Gruppen I
cites work: Theory of finite groups. An introduction
cites work: The Local Structure Theorem for Finite Groups with a Large 𝑝-Subgroup
cites work: Pushing up
cites work: Q5289092
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description: scientific article; zbMATH DE number 1924680