Wreath products of cyclic \(p\)-groups as automorphism groups.
type: Item
instance of: scholarly article
title: Wreath products of cyclic \(p\)-groups as automorphism groups.
zbMATH Open document ID: 1091.20027
author: Giovanni Cutolo
author: Howard Smith
author: James Wiegold
published in: Journal of Algebra
publication date: 2005-04-07T00:00:00Z
review text: The authors prove the following statement: The wreath product \(A\text{\,wr\,}B\) with cyclic \(p\)-groups \(A\) and \(B\) is the automorphism group of a group \(G\) iff \(A\) is of order 2 and \(B\) is of order 2 or 4. The group \(G\) is in the first case \(D_8\) or \(C_4\times C_2\) and in the second case some infinite nilpotent group of class 3, the possibilities are described completely.
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20F18
zbMATH DE Number: 2153377
zbMATH Keywords: nilpotent groups
zbMATH Keywords: automorphism groups
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: wreath products
reviewed by: Hermann Heineken
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.08.023
OpenAlex ID: W2088237159
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DOI: 10.1016/J.JALGEBRA.2003.08.023
description: scientific article; zbMATH DE number 2153377