Locally (soluble-by-finite) groups with all proper non-nilpotent subgroups of finite rank
type: Item
instance of: scholarly article
title: Locally (soluble-by-finite) groups with all proper non-nilpotent subgroups of finite rank
zbMATH Open document ID: 0927.20017
DOI: 10.1016/S0022-4049(97)00132-1
author: Martyn Dixon
author: Martin J. Evans
author: Howard Smith
published in: Journal of Pure and Applied Algebra
publication date: 1999-12-08T00:00:00Z
review text: The authors consider the intersection of the class mentioned in the title with classes \(N^*_c\) and \((A^2)^*\), where the star means every proper non-\(N_c\) (non-\(A^2\)) subgroup has finite rank. Example (Theorem A): Let \(G\) be a locally (soluble-by-finite) group in the class \(N^*_c\) for some positive integer \(c\). Then either \(G\in N_c\) or \(G\) has finite rank. Further interesting results are found on conjunctions with the closure with respect to local systems, sub-Cartesian products, ascending and descending normal series of the class of locally graded periodic groups.
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 1308299
zbMATH Keywords: subgroups of finite rank
zbMATH Keywords: locally (soluble-by-finite) groups
zbMATH Keywords: local systems
zbMATH Keywords: sub-Cartesian products
zbMATH Keywords: descending normal series
zbMATH Keywords: locally graded periodic groups
reviewed by: Hermann Heineken
MaRDI profile type: Publication
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full work available at URL: s0022-4049(97)00132-1
OpenAlex ID: W2090012617
description: scientific article; zbMATH DE number 1308299