Generating wreath products and their augmentation ideals
type: Item
instance of: scholarly article
title: Generating wreath products and their augmentation ideals
zbMATH Open document ID: 0898.20018
author: Andrea Lucchini
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1998-06-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108450
review text: For a group \(W\), let \(d(W)\) denote the minimum of the cardinalities of the generating sets of \(W\). The author studies \(d(W)\) for the wreath product \(W=H\wr G\) of a group \(H\) and a finite permutation group \(G\). He obtains formulas for \(d(W)\) when \(H\) is a finite soluble group and \(G\) is a transitive permutation group, or \(H\) is a nontrivial abelian group and \(G\) is the symmetric group. In addition, the author studies \(d(I_W)\), where \(d(I_W)\) denotes the minimum number of generators of the augmentation ideal \(I_W\) of the group ring \(ZW\) as a \(ZW\)-module.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 1115652
zbMATH Keywords: generating sets
zbMATH Keywords: wreath products
zbMATH Keywords: finite permutation groups
zbMATH Keywords: finite soluble groups
zbMATH Keywords: symmetric groups
zbMATH Keywords: numbers of generators
zbMATH Keywords: augmentation ideals
zbMATH Keywords: group rings
reviewed by: S. V. Mihovski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1115652