Recursive differentiability of linear k-quasigroups (k ≥ 2) is studied
in the present work. A k-quasigroup is recursively r-differentiable (r is a natu-
ral number) if its recursive derivatives of order up to r are quasigroup operations.
We give necessary and sufficient conditions of recursive 1-differentiability (respectively,
r-differentiability) of the k-group (Q, B), where B(x1, ..., xk) = x1 · x2 · ... ·
xk, ∀x1, x2, ..., xk ∈ Q, and (Q, ·) is a finite binary group (respectively, a finite abelian
binary group). The second result is a generalization of a known criterion of recursive
r-differentiability of finite binary abelian groups [4]. Also we consider a method of
construction of recursively r-differentiable finite binary quasigroups of high order r.
The maximum known values of the parameter r for binary quasigroups of order up to
200 are presented.
