On the automorphism groups of a special class of quasigroups
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)].
scientific article; zbMATH DE number 933264