Group isotopes and a holomorphic action.
type: Item
instance of: scholarly article
title: Group isotopes and a holomorphic action.
zbMATH Open document ID: 1190.20049
author: Aleš Drápal
published in: Results in Mathematics
publication date: 2009-11-02T00:00:00Z
review text: The author investigates the isomorphism problem with respect to all quasigroups isotopic to a given loop. This leads naturally to an action of the holomorph of a group \(G\) upon pairs \((a,b)\) of permutations of \(G\) in which \(a(1)=1\). That isomorphism classes correspond to orbits is new, but, the idea is essentially the same as the procedure described by \textit{F. M. Sokhats'kij} [in Ukr. Math. J. 48, No. 2, 283-293 (1996); translation from Ukr. Mat. Zh. 48, No. 2, 251-259 (1996; Zbl 0941.20070)]. The interest of the author in classification tools has been partly motivated by recent applications of quasigroups in the design of stream ciphers [see \textit{D. Gligoroski} et al., ``Edon80-hardware synchronous stream ciphers'', Symmetric Key Encryption Workshop, Aarhus, Denmark, May 2005], and hash functions [see \textit{D. Gligoroski} and \textit{S. J. Knapskog}, Commentat. Math. Univ. Carol. 49, No. 2, 219-239 (2008; Zbl 1201.94084)].
reviewed by: C. Pereira da Silva
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 08A05
zbMATH DE Number: 5624105
zbMATH Keywords: quasigroups isotopic to loops
zbMATH Keywords: T-quasigroups
zbMATH Keywords: isotopisms
zbMATH Keywords: central quasigroups
zbMATH Keywords: groups
zbMATH Keywords: isotopes
zbMATH Keywords: holomorphic actions
MaRDI profile type: Publication
full work available at URL: s00025-009-0370-4
OpenAlex ID: W2042896486
Wikidata QID: Q122152154
DOI: 10.1007/S00025-009-0370-4
description: scientific article; zbMATH DE number 5624105