The existence of \(J_ 3\) and its embeddings in \(E_ 6\)
type: Item
instance of: scholarly article
title: The existence of \(J_ 3\) and its embeddings in \(E_ 6\)
zbMATH Open document ID: 0703.20013
DOI: 10.1007/BF00147344
author: Michael Aschbacher
published in: Geometriae Dedicata
publication date: 1990-01-01T00:00:00Z
review text: The author determines the embeddings of the third sporadic group \(J_ 3\) of Janko in simple Chevalley groups of type \(E_ 6\) over finite and algebraically closed fields. As a corollary he obtains a short elegant existence proof of \(J_ 3\). This is of interest as \(J_ 3\) is one of the few sporadic groups not contained in the Monster, so its existence cannot be verified within that group. Previous existence proofs (see the papers of \textit{G. Higman} and \textit{J. McKay} [Bull. Lond. Math. Soc. 1, 89-94 (1969; Zbl 0175.30103)] and \textit{R. Weiss} [Math. Z. 179, 91-95 (1982; Zbl 0481.05034)]) were highly computational. P. Kleidman and R. Wilson were the first to prove that \(J_ 3\) embeds in \(E_ 6(4)\). Their proof was machine aided.
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 4152676
zbMATH Keywords: embeddings
zbMATH Keywords: third sporadic group \(J_ 3\) of Janko
zbMATH Keywords: simple Chevalley groups of type \(E_ 6\)
zbMATH Keywords: existence proof
reviewed by: Andreiy Kondrat'yev
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147344
OpenAlex ID: W2913928285
description: scientific article; zbMATH DE number 4152676