\(K\)-groups and wreath products.
type: Item
instance of: scholarly article
title: \(K\)-groups and wreath products.
zbMATH Open document ID: 1119.20030
author: Mauro Costantini
author: G. Zacher
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2007-04-26T00:00:00Z
review text: A group is called a \(K\)-group if its subgroup lattice is a complemented lattice. All finite simple groups are \(K\)-groups. On the other hand, the structure of finite soluble \(K\)-groups has been characterized by one of the authors long time ago, [\textit{G. Zacher}, Rend. Sem. Mat. Univ. Padova 22, 113-122 (1953; Zbl 0051.25802)]. However, in the general case there is no characterization of such groups. In the article under review, the authors give several criteria for a wreath product to be a \(K\)-group.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E22
zbMATH DE Number: 5147111
zbMATH Keywords: complemented groups
zbMATH Keywords: wreath products
zbMATH Keywords: subgroup lattices
zbMATH Keywords: complemented lattices
reviewed by: Igor Subbotin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5147111