Factorizations of the groups \(G_ 2(q)\)
type: Item
instance of: scholarly article
title: Factorizations of the groups \(G_ 2(q)\)
zbMATH Open document ID: 0544.20012
DOI: 10.1007/BF01237856
author: K. B. Tchakerian
author: Ts. R. Gentchev
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: Let \(G_ 2(q)\) be the (simple) group of Lie type \((G_ 2)\) over the finite field GF(q). The following result is proved. Theorem. Let \(G=G_ 2(q)\) and \(G=AB\) where A, B are proper non-Abelian simple subgroups of G. Then one of the following holds: (1) \(q=4\) and \(A\cong HJ\), \(B\cong U_ 3(4)\); (2) \(q=3^ n\) and \(A\cong L_ 3(q)\), \(B\cong U_ 3(q)\); (3) \(q=3^{2n+1}>3\) and \(A\cong L_ 3(q)\), \(B\cong^ 2G_ 2(q)\). The factorizations (1)-(3) exist. In the above, HJ is the Hall-Janko simple group, \(L_ 3(q)\) and \(U_ 3(q)\) denote respectively \(PSL_ 3(q)\) and \(PSU_ 3(q^ 2)\), and \({}^ 2G_ 2(q)\) is the Ree group of characteristic 3. This result has been proved independently U. Preiser.
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 3865550
zbMATH Keywords: group of Lie type
zbMATH Keywords: simple subgroups
zbMATH Keywords: factorizations
zbMATH Keywords: Hall-Janko simple group
Wikidata QID: Q114233980
MaRDI profile type: Publication
cites work: The conjugate classes of Chevalley groups of type \((G_2)\)
cites work: Q5652887
cites work: Q4163377
cites work: The maximal subgroups of \(G_ 2(\)4)
cites work: Q4740081
cites work: Factorizations of finite groups
cites work: A Family of Simple Groups Associated with the Simple Lie Algebra of Type (G 2 )
cites work: On products of finite simple groups
description: scientific article; zbMATH DE number 3865550