ON RECURSIVE DIFFERENTIABILITY OF BINARY QUASIGROUPS

Inga LARIONOVA-COJOCARU, Parascovia SYRBU Moldova State University

Abstract

Recursively differentiable binary quasigroups and loops, are considered in the present paper. Invariants under the recursive differentiability of binary quasigroups are found. It is shown that the recursive derivative of order one of an LIP-loop (Q,⋅) (in particular of a left Bol loop) is an isostrophe of its core. The recursively 1-differentiable left Bol loops are studied. Some properties of recursive derivatives of order one of left Bol loops are established. Keywords: Recursively differentiable quasigroup, recursive derivative, isostrophe, core, LIP-loop, left Bol loop.