Groups and nilpotent Lie rings whose order is the sixth power of a prime.
type: Item
instance of: scholarly article
title: Groups and nilpotent Lie rings whose order is the sixth power of a prime.
zbMATH Open document ID: 1072.20022
author: M. F. Newman
author: E. A. O'Brien
author: Michael Vaughan-Lee
published in: Journal of Algebra
publication date: 2004-09-23T00:00:00Z
review text: The authors give a complete description (up to isomorphism) of all finite \(p\)-groups of order \(p^6\) (available via computer systems). The result is achieved independently of previous attempts of various authors, which contained errors. On the other hand, the reliability of the results is partially confirmed by some of the previous results. The main difficulty is to distinguish different isomorphism types, while a complete list with possible repeats is comparatively easy to obtain. The new ingredient is finding first a similar complete description of nilpotent Lie rings of order \(p^6\), and then using the Baker-Campbell-Hausdorff formula when the nilpotency class is less than \(p\) (the only case not covered by this scheme -- that of \(5\)-groups of class \(5\) of order \(5^6\) -- was known earlier). For the history of earlier attempts see the extensive survey in the paper.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 20F40
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 2102506
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: nilpotent Lie rings
zbMATH Keywords: Baker-Campbell-Hausdorff formula
zbMATH Keywords: power-commutator presentations
zbMATH Keywords: groups of order \(p^6\)
Wikidata QID: Q115351772
reviewed by: Evgenii I. Khukhro
describes a project that uses: GAP
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.11.012
OpenAlex ID: W2023646834
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DOI: 10.1016/J.JALGEBRA.2003.11.012
description: scientific article; zbMATH DE number 2102506