Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$

In the paper, we prove the $\alpha$-completeness of finite systems of function of $k$-valued logic for $k=3,4$ containing all permutations of the symmetric group $S_k$ on the set $E_k=\{0,1,\dots,k-1\}$, the operation of addition modulo $k$, and $k$ certain binary operation. This result is extended to some other systems of functions which are obtained by replacing the operation of addition by some quasi-group operation.