A characterization of solvability for finite groups in terms of their frame.
type: Item
instance of: scholarly article
title: A characterization of solvability for finite groups in terms of their frame.
zbMATH Open document ID: 1179.20017
author: Francesco Fumagalli
published in: Journal of Algebra
publication date: 2009-10-13T00:00:00Z
review text: The following interesting characterization of finite solvable groups \(G\) in terms of their poset \(C(G)\) of conjugacy classes of subgroups is proved: ``A finite group \(G\) is solvable if and only if every collection of coatoms of \(C(G)\) has a well-defined meet and the poset consisting of all such meets is a modular lattice''.
reviewed by: Marius Tărnăuceanu
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 5614694
zbMATH Keywords: finite solvable groups
zbMATH Keywords: conjugacy classes
zbMATH Keywords: maximal subgroups
zbMATH Keywords: posets of subgroups
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.06.005
OpenAlex ID: W2031260425
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DOI: 10.1016/J.JALGEBRA.2009.06.005
description: scientific article; zbMATH DE number 5614694