Generalizing poliadic operations

For any integers $l\geqslant 2$, $k\geqslant 2$, of a subset $T$ of the symmetric group $\mathbf{S}_k$ and semi-group $A$ on the Cartesian product $T\times A^k$ an $l$-ary operation $[\,]_{l, T, k}$ is determined. This $l$-ary operation is similar to the Post poliadic operations, which he defined on the set of poliadic permulations. In the paper the properties of the operation $[\,]_{l, T, k}$ are studied.