Characters of finite quasigroups
type: Item
instance of: scholarly article
title: Characters of finite quasigroups
zbMATH Open document ID: 0537.20042
DOI: 10.1016/S0195-6698(84)80017-7
published in: European Journal of Combinatorics
publication date: 1984-01-01T00:00:00Z
review text: In this paper the authors study some of the basics of a character theory for finite non-empty quasigroups, generalizing the traditional ordinary character theory for groups. The authors present the relevant notions from quasigroup theory (the multiplication group, quasigroup conjugacy classes, and the space of class functions) which enable one to apply these theories to quasigroups. Quasigroup characters as class functions and the character table of a quasigroup are given explicitly, and the characters are seen to form an orthonormal basis for the space of class functions. Main result: the character table of a finite quasigroup Q specifies the congruence lattice of Q.
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 3853371
zbMATH Keywords: multiplication group
zbMATH Keywords: quasigroup conjugacy classes
zbMATH Keywords: space of class functions
zbMATH Keywords: Quasigroup characters
zbMATH Keywords: character table
zbMATH Keywords: finite quasigroup
zbMATH Keywords: congruence lattice
author: Kenneth Johnson
author: J. D. H. Smith
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
cites work: On pseudo groups
cites work: Contributions to the Theory of Loops
cites work: Q5515384
cites work: Q4050760
cites work: Q4183464
cites work: Q5515373
cites work: Q3214832
cites work: Q5340151
cites work: Q5707657
cites work: Double coset and orbit spaces
cites work: Coherent configurations. I: Ordinary representation theory
cites work: Q4103728
cites work: Q3913571
cites work: Loop transversals and the centralizer ring of a permutation group
cites work: Q4161482
cites work: Centraliser rings of multiplication groups on quasigroups
cites work: Mal'cev varieties
cites work: S-Ringe und verallgemeinerte Charaktere auf endlichen Gruppen
cites work: On Schur-rings which define a proper character theory on finite groups
cites work: Q5512231
full work available at URL: s0195-6698(84)80017-7
OpenAlex ID: W2038862321
description: scientific article; zbMATH DE number 3853371