On the automorphism groups of a special class of quasigroups
type: Item
instance of: scholarly article
title: On the automorphism groups of a special class of quasigroups
zbMATH Open document ID: 0861.20059
DOI: 10.1007/BF03322188
author: Herbert Zeitler
author: Juraj Šiftar
published in: Results in Mathematics
publication date: 1997-04-09T00:00:00Z
review text: The authors investigate automorphism groups of 2-generated quasigroups, constructed by \textit{J. Šiftar} [in Glasn. Mat., III. Ser. 18(38), 217-219 (1983; Zbl 0537.20044)] and show that such quasigroups of odd order \(k\geq 7\) have only one nontrivial automorphism, whereas in the case of even order \(k\geq 6\) there are no nontrivial automorphisms. \(A^k_n\)-quasigroups have been investigated by various authors, because of their interesting algebraic properties as well as their interpretation in terms of finite geometries. The importance of automorphisms of 2-generated quasigroups is apparent in the paper of \textit{Sh. K. Stein} [Pac. J. Math. 14, 1091-1102 (1964; Zbl 0132.26502)].
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 933264
zbMATH Keywords: automorphism groups
zbMATH Keywords: 2-generated quasigroups
zbMATH Keywords: \(A^ k_ n\)-quasigroups
zbMATH Keywords: finite geometries
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
cites work: On the problem of existence of finite regular planes
cites work: Homogeneous quasigroups
cites work: On affine planes over \(A_n^k\)-quasigroups
description: scientific article; zbMATH DE number 933264