Quasigroup actions: Markov chains, pseudoinverses, and linear representations
type: Item
instance of: scholarly article
title: Quasigroup actions: Markov chains, pseudoinverses, and linear representations
zbMATH Open document ID: 0944.20059
author: J. D. H. Smith
published in: Southeast Asian Bulletin of Mathematics
publication date: 2000-09-18T00:00:00Z
review text: This paper initiates the extension to quasigroups of a further aspect of group representation theory: transitive permutation representations. Using pseudoinverses of incidence matrices of quasigroups in partitions induced by left multiplications of subquasigroups, a transitive permutation action of a quasigroup is defined as a set of Markov chain actions indexed by the quasigroup. Finally, Burnside's lemma for transitive quasigroup actions is derived.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20B05
Mathematics Subject Classification ID: 20M30
zbMATH DE Number: 1406305
zbMATH Keywords: Latin squares
zbMATH Keywords: transitive permutation representations
zbMATH Keywords: pseudoinverses
zbMATH Keywords: incidence matrices
zbMATH Keywords: quasigroups
zbMATH Keywords: partitions
zbMATH Keywords: Markov chain actions
zbMATH Keywords: transitive quasigroup actions
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1406305