On sets of generators of $l$-ary group $\langle A^k, [\ ]_{l,\sigma,k}\rangle$. I

The relationship between sets of generators in group $A$ and sets of generators in polyadic group $\langle A^k, [\ ]_{l,\sigma,k}\rangle$ with $l$-ary operation $[\ ]_{l,\sigma,k}$, that is defined on Cartesian power $A^k$ of group $A$ for arbitrary integer $l\geqslant 2$ and arbitrary substitution $\sigma$ from the set $\mathbf{S}_k$ of all substitutions of the set $\{1, 2,\dots, k\}$ is described.