A classification of regular \(p\)-groups with invariants \((e,2,1)\)
type: Item
instance of: scholarly article
title: A classification of regular \(p\)-groups with invariants \((e,2,1)\)
zbMATH Open document ID: 0999.20014
author: Youhu Ji
author: Shaofei Du
author: Lingling Zhang
published in: Southeast Asian Bulletin of Mathematics
publication date: 2002-05-30T00:00:00Z
review text: Elements \(b_1,\dots,b_r\) are said to form a \(U\)-basis of a finite \(p\)-group \(G\) if every element of \(G\) has a unique representation as a product \(b_1^{k_1}\cdots b_r^{k_r}\), where \(0\leq k_i<|b_i|\). By P.~Hall's theorem every regular \(p\)-group \(G\) has a \(U\)-basis and the set of orders of its elements is an invariant of \(G\), called \(e\)-invariants. The present paper contains a complete classification (up to isomorphism) of regular \(p\)-groups with \(e\)-invariants \(\{n,2,1\}\).
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 1747996
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: regular \(p\)-groups
zbMATH Keywords: element orders
reviewed by: Evgenii I. Khukhro
MaRDI profile type: Publication
full work available at URL: s10012-001-0245-4
OpenAlex ID: W2084310904
DOI: 10.1007/S10012-001-0245-4
description: scientific article; zbMATH DE number 1747996