Characteristic properties of σ-A-nuclei of a quasigroup

Abstract

In this paper, we investigate the properties of [Formula: see text]-A-nuclei of a quasigroup including relations between them and relations between their respective component sets, where [Formula: see text]. We also find connections between components of [Formula: see text]-A-nuclei of a quasigroup and components of [Formula: see text]-A-nuclei of the isostrophic images. Further, we investigate the properties of various inverse quasigroups using the derived connections. These properties will not only make the study of [Formula: see text]-A-nuclei of a quasigroup simple but also reduce the time required in the computation of [Formula: see text]-A-nuclei of a quasigroup for different values of [Formula: see text].