Frucht theorem for inverse semigroups
type: Item
instance of: scholarly article
title: Frucht theorem for inverse semigroups
zbMATH Open document ID: 0923.20047
DOI: 10.1007/BF02355729
author: N. A. Nemirovskaya
published in: Mathematical Notes
publication date: 1999-03-23T00:00:00Z
review text: The main result is the following: For any finite inverse semigroup \(S\) there exists a weighted graph \(\Gamma\) such that \(\text{PAut}_\omega\Gamma\cong S\). Here a graph is undirected without loops with vertex set \(V(\Gamma)\) and edge set \(E(\Gamma)\) and weight function \(\omega\colon V(\Gamma)\to P\) where \(P\) is a lower semilattice. \(\text{PAut}_\omega\) denotes the set of partial automorphisms of \(\Gamma\), i.e., partial injective mappings which preserve and reflect edges of \(\Gamma\) with the additional property that \(\omega(a)=\omega(b)\) for a partial automorphism \(\varphi\) implies \(\omega(\varphi(a))=\omega(\varphi(b))\) and \(\omega(a)<\omega(b)\) implies \(\omega(\varphi(a))<\omega(\varphi(b))\) if \(\varphi(a)\) and \(\varphi(b)\) are defined.
reviewed by: Ulrich Knauer
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20M20
zbMATH DE Number: 1238012
zbMATH Keywords: finite inverse semigroups
zbMATH Keywords: partial transformations
zbMATH Keywords: graphs
zbMATH Keywords: Frucht theorem
zbMATH Keywords: partial automorphisms
MaRDI profile type: Publication
cites work: Q5771659
cites work: Semigroups of mappings on graphs
cites work: Q3831034
cites work: Q3848243
full work available at URL: https://doi.org/10.1007/bf02355729
OpenAlex ID: W2077891165
description: scientific article; zbMATH DE number 1238012