Automorphisms of iterated wreath product \(p\)-groups.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1252.20024
DOI: 10.4153/CMB-2011-088-3
author: Jeffrey M. Riedl
published in: Canadian Mathematical Bulletin
publication date: 2012-06-04T00:00:00Z
full work available at URL: CMB-2011-088-3
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 6042610
zbMATH Keywords: wreath products
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: automorphism groups
zbMATH Keywords: character theory
zbMATH Keywords: finite general linear groups
zbMATH Keywords: orders of groups of automorphisms
MaRDI profile type: Publication
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title: Automorphisms of iterated wreath product \(p\)-groups.
review text: Let \(W=(\cdots((\mathbb Z_{p^e}\wr\mathbb Z_p)\wr\mathbb Z_p)\cdots\wr\mathbb Z_p)\) be an (\(n\) times) iterated regular wreath product, well-known to be isomorphic to a \(p\)-Sylow subgroup of the linear group \(\text{GL}_{p^{{n-1}}}(q)\), where \(p\mid q-1\), and the \(p\)-part of \(q-1\) is \(p^e\geq 3\). The author determines the order of the automorphism group \(\Aut(W)\) using a method based on representation theory, namely, the author's automorphism counting formula [J. Algebra 322, No. 12, 4483-4497 (2009; Zbl 1193.20026)].NEWLINENEWLINE In the second part of the paper several properties of characters of the group \(W\) are established.
reviewed by: János Kurdics
description: scientific article; zbMATH DE number 6042610