Solvability of finite coatomic groups
type: Item
instance of: scholarly article
title: Solvability of finite coatomic groups
zbMATH Open document ID: 0715.20012
DOI: 10.1007/BF01157285
author: Anatoli Kondrat'ev
published in: Mathematical Notes
publication date: 1990-01-01T00:00:00Z
review text: \textit{F. Menegazzo} [Atti Accad. Naz. Lincei., Rend., Cl. Sci. Fis. Mat. Nat., VIII. Ser. 48, 559-562 (1970; Zbl 0216.088)] introduced the class of IM-groups (they are also called coatomic groups), i.e. groups in which every proper subgroup is the intersection of some maximal subgroups. He also determined all finite solvable coatomic groups. Further \textit{F. Migliorini} [Matematiche 29, 231-248 (1974; Zbl 0336.20018)], \textit{M. Bianchi} and \textit{M. C. Tamburini Bellani} [Rend., Sci. Mat. Appl., A 111, 429-436 (1977; see the preceding review Zbl 0715.20011)] obtained criteria for nonsimplicity of the finite coatomic groups. The question of existence of finite nonsolvable coatomic groups remained open. In this paper it is proved the solvability of finite coatomic groups whose simple sections are known simple groups.
reviewed by: Andreiy Kondrat'yev
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 4177365
zbMATH Keywords: intersections of maximal subgroups
zbMATH Keywords: IM-groups
zbMATH Keywords: finite solvable coatomic groups
zbMATH Keywords: solvability
zbMATH Keywords: simple sections
zbMATH Keywords: simple groups
MaRDI profile type: Publication
cites work: Q5619247
cites work: Q4104140
cites work: Q5662096
cites work: Q3993211
cites work: Q3684278
cites work: Subgroups of Classical Groups Generated by Long Root Elements
cites work: The 2-Transitive Permutation Representations of the Finite Chevalley Groups
cites work: Involutions in Chevalley groups over fields of even order
cites work: Some subgroups of GL(n,2) generated by involutions. I
cites work: Flag-transitive subgroups of Chevalley groups
cites work: Linear groups containing a Singer cycle
cites work: Minimal degree for a permutation representation of a classical group
cites work: Overgroups of Sylow subgroups in sporadic groups
cites work: The geometry of root subgroups in exceptional groups. II
full work available at URL: https://doi.org/10.1007/bf01157285
OpenAlex ID: W2088733140
description: scientific article; zbMATH DE number 4177365