Group isotopes and a holomorphic action.
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)].
scientific article; zbMATH DE number 5624105