Factorizations of finite groups
type: Item
instance of: scholarly article
title: Factorizations of finite groups
zbMATH Open document ID: 0536.20013
DOI: 10.1007/BF01215047
author: Udo Preiser
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173409
review text: The main result of the paper under review is the following Theorem. Let G be a finite group which contains simple subgroups A and B with \(G=AB\). Assume that a Sylow 2-subgroup of A has rank 2 and a Sylow 2-subgroup of B is elementary Abelian. Then one of the following holds: (1) \(G=A\) or \(G=B\); (2) \(G\cong A\times B;\) (3) \(G\cong A_ 6\) and \(A\cong B\cong A_ 5;\) (4) \(G\cong A_ 7,\quad A\cong L_ 2(7)\) and \(B\cong A_ 5;\) (5) \(G\cong A_ 9,\quad A\cong A_ 6\) or \(A_ 7\), \(B\cong L_ 2(8);\) (6) \(G\cong M_{12},\quad A\cong M_{11},\quad B\cong A_ 5\) or \(L_ 2(11);\) (7) \(G\cong G_ 2(3^ m),\quad A\cong L_ 3(3^ m)\) and \(B\cong^ 2G_ 2(3^ m)\) for odd \(m\neq 1.\) The proof doesn't use the classification of finite simple groups. Remark: \textit{K. B. Tchakerian} and \textit{Ts. R. Gentchev} [Arch. Math. 41, 385-389 (1983; Zbl 0506.20011)] proved similar results in the case \(| A|_ 2\leq 8\) and \(| B|_ 2\leq 16\).
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D06
zbMATH DE Number: 3851359
zbMATH Keywords: simple subgroups
zbMATH Keywords: Sylow 2-subgroup
reviewed by: S. A. Syskin
MaRDI profile type: Publication
Wikidata QID: Q114234002
cites work: Sylow intersections and fusion
cites work: On finite factorizable groups
cites work: Q5662096
cites work: 2-fusion in finite groups
cites work: Q5577154
cites work: On finite groups with Sylow 2-subgroups of type \(\hat A_n,\;n=8,9,10 \) and \(11\)
cites work: Finite simple groups of low 2-rank and the families $G_2 \left( q \right),\,D_4^2 \left( q \right),\,q$ odd
cites work: Finite groups whose 2-subgroups are generated by at most 4 elements
cites work: Products of simple groups
cites work: On finite groups having self-centralizing 2-subgroups of small order
cites work: Endliche Gruppen I
cites work: Linear groups containing a Singer cycle
cites work: Finite simple groups in which a Sylow 2-subgroup is an extension of an abelian group by a group of rank 1
cites work: On the minimal degrees of projective representations of the finite Chevalley groups
cites work: Q5569508
cites work: A characterisation of the unitary groups \(PSU(4,q^ 2), q\) odd
cites work: Produkte von endlichen einfachen Gruppen
cites work: Products of \(A_5\) and a finite simple group
cites work: ABSTRACT PROPERTIES OF THE SIMPLE SPORADIC GROUPS
cites work: On products of finite simple groups
cites work: Products of finite simple groups
description: scientific article; zbMATH DE number 3851359