Semicomplete permutational wreath products
type: Item
instance of: scholarly article
zbMATH Open document ID: 0976.20020
author: John Panagopoulos
published in: Algebra Colloquium
publication date: 2002-01-07T00:00:00Z
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20D45
zbMATH DE Number: 1591266
zbMATH Keywords: semicomplete groups
zbMATH Keywords: permutational wreath products
zbMATH Keywords: automorphisms
MaRDI profile type: Publication
full work available at URL: s10011-000-0275-y
OpenAlex ID: W2032401428
DOI: 10.1007/S10011-000-0275-Y
title: Semicomplete permutational wreath products
review text: A group is called semicomplete if every automorphism which induces the identity on the factor commutator group is inner. In this paper the author studies the semicompleteness of the permutational wreath product \(W=A\text{ wr}(H)B\), \(B\) finite and \(H\) a subgroup of \(B\). The main result states that if \(W\) is semicomplete then \(A\) is semicomplete and \(N_B(H)=H\cdot Z(B)\). Here, as usual, \(N_B(H)\) is the normalizer of \(H\) in \(B\) and \(Z(B)\) the centre of \(B\). Among the corollaries is an old result of the author concerning automorphisms of standard wreath products [Arch. Math. 37, 499-511 (1981; Zbl 0458.20027)].
description: scientific article