A coalgebraic approach to quasigroup permutation representations.
type: Item
instance of: scholarly article
title: A coalgebraic approach to quasigroup permutation representations.
zbMATH Open document ID: 1068.20070
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: The paper is devoted to permutation representations of finite quasigroups. The class of all permutation representations of a given finite quasigroup is identified with a covariety of coalgebras. Each permutation representation decomposes as a sum of homomorphic images of homogeneous spaces. For groups, permutation representations in the sense presented specialize to the classical concept. Also Burnside's Lemma is extended from groups to quasigroups.
reviewed by: Radomír Halaš
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 08C05
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 2158819
zbMATH Keywords: loops
zbMATH Keywords: finite quasigroups
zbMATH Keywords: permutation representations
zbMATH Keywords: covarieties of coalgebras
author: J. D. H. Smith
MaRDI profile type: Publication
full work available at URL: s000120200010
OpenAlex ID: W2061501541
DOI: 10.1007/S000120200010
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description: scientific article; zbMATH DE number 2158819