We study the generic nature of simplicity, non-affinity and polynomial completeness of finite n -quasigroups. It is shown that for fixed n almost all n -quasigroups are strongly non-affine, i.e., not isotopic to affine n -quasigroups. Exact number of simple, affine and simultaneously simple and affine n -quasigroups of the order 4 is established. As a corollary, it is proven that almost all n -quasigroups of the order 4 are polynomially complete and strongly non-affine.
No takes yet. Share an insight, caveat, or question.
Galatenko et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: