Schur multiplicators of finite \(p\)-groups with fixed coclass.
type: Item
instance of: scholarly article
title: Schur multiplicators of finite \(p\)-groups with fixed coclass.
zbMATH Open document ID: 1153.20015
author: B. Eick
published in: Israel Journal of Mathematics
publication date: 2008-10-16T00:00:00Z
review text: The author investigates the Schur multiplicators \(M(G)\) of finite \(p\)-groups \(G\) using the coclass as primary invariant (the coclass of a group of order \(p^n\) and class \(c\) is \(n-c\)). For \(p>2\), she proves that there are at most finitely many \(p\)-groups \(G\) of coclass \(r\) with \(|M(G)|\leq s\) for every \(r\) and \(s\). This is not true for \(p=2\). Infinite series of 2-groups \(G\) with coclass \(r\) and trivial Schur multiplicator are constructed. Coclass theory is used to further investigate the Schur multiplicators of 2-groups of coclass \(r\).
reviewed by: Andrea Lucchini
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5351778
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: coclass
zbMATH Keywords: Schur multiplicators
zbMATH Keywords: pro-\(p\)-groups
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: s11856-008-1025-y
OpenAlex ID: W2072499892
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DOI: 10.1007/S11856-008-1025-Y
description: scientific article; zbMATH DE number 5351778