All automorphisms of \({\mathcal F}P^+(S_n)\) are inner
type: Item
instance of: scholarly article
title: All automorphisms of \({\mathcal F}P^+(S_n)\) are inner
zbMATH Open document ID: 0961.20051
author: Volodymyr Mazorchuk
published in: Semigroup Forum
publication date: 2001-03-06T00:00:00Z
review text: Let \({\mathcal B}(S_n)\) be the semigroup of all subsets of the symmetric group \(S_n\), with the induced action. Define an equivalence \(\sim\) on \({\mathcal B}(S_n)\) by setting \(A\sim B\) if for any \(x\in\{1,2,\ldots,n\}\) the sets \(\{\sigma(x)\mid\sigma\in A\}\) and \(\{\sigma(x)\mid\sigma\in B\}\) coincide. The quotient \({\mathcal B}(S_n)/ \sim\) is denoted by \({\mathcal F}P(S_n)\). It is proved that all automorphisms of the semigroup \({\mathcal F}P^+(S_n)={\mathcal F}P(S_n)\setminus\emptyset\) are inner.
reviewed by: Peeter Normak
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 1445566
zbMATH Keywords: power semigroups
zbMATH Keywords: symmetric groups
zbMATH Keywords: automorphisms
MaRDI profile type: Publication
full work available at URL: s002339910040
OpenAlex ID: W2007285012
DOI: 10.1007/S002339910040
description: scientific article; zbMATH DE number 1445566