Groups of type \([d\to 3(d-1)]\).
type: Item
instance of: scholarly article
title: Groups of type \([d\to 3(d-1)]\).
zbMATH Open document ID: 0696.20030
DOI: 10.1007/BF01200031
author: Gérard Endimioni
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: Let \(d\) be a fixed integer and \(G\) a group whose \(d\)-generator subgroups are nilpotent of class at most \(3(d-1)\). Then, with a hypothesis on the order of the elements, we prove that \(G\) is nilpotent, of class bounded in terms of \(d\). Examples show that the hypothesis on the order of the elements is necessary.
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 4140034
zbMATH Keywords: \(d\)-generator subgroups
zbMATH Keywords: order
zbMATH Keywords: nilpotent groups
zbMATH Keywords: class
MaRDI profile type: Publication
cites work: Third Engel groups and the Macdonald-Neumann conjecture
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cites work: Q5817437
cites work: Residual Properties of Infinite Soluble Groups
cites work: Engelsche Elemente der Länge drei. (Engel elements of length three.)
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full work available at URL: https://doi.org/10.1007/bf01200031
OpenAlex ID: W2070143030
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description: scientific article; zbMATH DE number 4140034