Automorphisms of a finitary factor power of an infinite symmetric group

We consider a semigroup FP_\textfin⁺ ( \mathfrakS_\textfin( \mathbbN ) ) FP_{\text{fin}}^{+} \left( {{\mathfrak{S}_{\text{fin}}}\left( \mathbb{N} \right)} \right) defined as a finitary factor power of a finitary symmetric group of countable order. It is proved that all automorphisms of FP_\textfin⁺ ( \mathfrakS_\textfin( \mathbbN ) ) FP_{\text{fin}}^{+} \left( {{\mathfrak{S}_{\text{fin}}}\left( \mathbb{N} \right)} \right) are induced by permutations from \mathfrakS( \mathbbN ) \mathfrak{S}\left( \mathbb{N} \right) .