Frobenius quasigroups and regular polygons.
type: Item
instance of: scholarly article
title: Frobenius quasigroups and regular polygons.
zbMATH Open document ID: 1065.20078
DOI: 10.1007/BF03323381
author: Oddvar Iden
author: Karl Strambach
published in: Results in Mathematics
publication date: 2004-11-26T00:00:00Z
review text: The authors discuss in this paper which conditions force a Frobenius quasigroup to have a multiplication that is one of the geometric multiplications defined by the regular \(n\)-gons. Topological Frobenius quasigroups \(Q\) homeomorphic to a connected topological variety as well as algebraic connected Frobenius quasigroups are of this type if they have no epimorphic image with left translations of the same order as \(Q\). Beside of this they characterize properties considered in the theory of quasigroups within the Frobenius group \(G\) generated by the left translations of a Frobenius quasigroup \(Q\).
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 51H20
Mathematics Subject Classification ID: 51H30
Mathematics Subject Classification ID: 22A30
zbMATH DE Number: 2119245
zbMATH Keywords: Frobenius groups
zbMATH Keywords: left distributive quasigroups
zbMATH Keywords: left translations
zbMATH Keywords: topological Frobenius quasigroups
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2119245