ON RECURSIVE DIFFERENTIABILITY OF BINARY QUASIGROUPS

Abstract

A quasigroup is called recursively n-differentiable if its first n recursive derivatives are quasigroups. The class of recursively differential quasigroups is arisen in the theory of MDS codes, in early 2000. Connections between recursive derivatives of different order are found in the present work. It is shown that isomorphic quasigroups have isomorphic recursive derivatives of any order. Also, it is proved that, if the recursive derivative of order one of a finite quasigroup (Q, ·) is commutative, then its group of inner mappings is a subgrup of the group of inner mappings of (Q, ·), of the same index as their corresponding multiplication groups.