Finite \(n\)-coverings of groups
type: Item
instance of: scholarly article
title: Finite \(n\)-coverings of groups
zbMATH Open document ID: 0816.20025
DOI: 10.1007/BF01196666
author: Marc A. Brodie
published in: Archiv der Mathematik
publication date: 1995-07-17T00:00:00Z
review text: An \(n\)-covering is meant as a generalization of a covering in the sense that every \(n\)-tuplet of elements is contained in one of the members of the \(n\)-covering. B. H. Neumann's Lemma on finite coverings has its analogue for \(n\)-coverings (Lemma 2.3). The group \(G\) possesses a finite non-trivial \(n\)-covering of subgroups (normal subgroups) if and only if \(G\) has a homomorphic image which is not generated by \(n\) elements and finite (elementary abelian), see section 2. Coverings by subgroups belonging to varieties are considered in their consequences to the group \(G\) itself in section 3, especially for properties near to nilpotency.
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 701013
zbMATH Keywords: coverings by subgroups
zbMATH Keywords: finite coverings
zbMATH Keywords: \(n\)-coverings
zbMATH Keywords: \(n\)-covering of subgroups
zbMATH Keywords: varieties
zbMATH Keywords: nilpotency
reviewed by: Hermann Heineken
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 701013