The groups of exponent p and order \(p^ 7\) (p any prime)
type: Item
instance of: scholarly article
title: The groups of exponent p and order \(p^ 7\) (p any prime)
zbMATH Open document ID: 0651.20025
DOI: 10.1016/0021-8693(88)90051-8
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: This paper aims to give a list of groups of exponent p and order \(p^ 7\) for all primes p. The list consists of commutator presentations on 7 generators. It is intended that each group of exponent p and order \(p^ 7\) be isomorphic to exactly one group in the list. This intention is not achieved. There is (at least one) duplication: group 117 is isomorphic to group 115 when 4 divides p-1 and to group 116 when 4 divides p-3. There are at least two groups which do not occur in the list. (I am indebted to D. B. Tyler for drawing my attention to these errors and E. A. O'Brien for helping to check them.)
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20-04
zbMATH DE Number: 4061497
zbMATH Keywords: nilpotent quotient algorithm
zbMATH Keywords: list of groups
zbMATH Keywords: exponent p
zbMATH Keywords: order \(p^ 7\)
zbMATH Keywords: commutator presentations
author: David Wilkinson
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90051-8
OpenAlex ID: W2026364505
cites work: Q3253828
cites work: Q3869534
cites work: The Groups of Order p 6 (p and Odd Prime)
cites work: The groups of order 128
description: scientific article; zbMATH DE number 4061497