Automorphisms of a finitary factor power of an infinite symmetric group

Abstract

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