Conjugacy of \(\text{Alt}_5\) and \(\text{SL}(2,5)\) subgroups of \(E_6(\mathbb{C})\), \(F_4(\mathbb{C})\), and a subgroup of \(\mathbb{E}_8(\mathbb{C})\) of type \(A_2E_6\)
type: Item
instance of: scholarly article
title: Conjugacy of \(\text{Alt}_5\) and \(\text{SL}(2,5)\) subgroups of \(E_6(\mathbb{C})\), \(F_4(\mathbb{C})\), and a subgroup of \(\mathbb{E}_8(\mathbb{C})\) of type \(A_2E_6\)
zbMATH Open document ID: 0908.20036
author: Darrin D. Frey
published in: Journal of Algebra
publication date: 1998-11-18T00:00:00Z
review text: Many mathematicians work on solving the embedding and conjugacy problems of finite quasisimple subgroups of exceptional Lie groups. In this paper, the author classifies alternating groups of degree 5 (denoted \(\text{Alt}_5\)) and \(\text{SL}(2,5)\) subgroups of \(E_6(\mathbb{C})\) and \(F_4(\mathbb{C})\) up to conjugacy. The results for \(E_6(\mathbb{C})\) are then used to classify \(\text{Alt}_5\) and \(\text{SL}_2(5)\) subgroups of the centralizer in \(E_8(\mathbb{C})\) of an element of type \(3B\) (a group of type \(A_2E_6\)) which allow to refine the main results in the author's Ph. D. Thesis.
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 1203867
zbMATH Keywords: finite quasisimple groups
zbMATH Keywords: exceptional Lie groups
zbMATH Keywords: embeddings
zbMATH Keywords: conjugacy
reviewed by: Anatoli Kondrat'ev
MaRDI profile type: Publication
full work available at URL: jabr.1997.7214
OpenAlex ID: W2101060539
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DOI: 10.1006/JABR.1997.7214
description: scientific article; zbMATH DE number 1203867