All automorphisms of \({\mathcal F}P^+(S_n)\) are inner
Let \({\mathcal B}(S_n)\) be the semigroup of all subsets of the symmetric group \(S_n\), with the induced action. Define an equivalence \(\sim\) on \({\mathcal B}(S_n)\) by setting \(A\sim B\) if for any \(x\in\{1,2,\ldots,n\}\) the sets \(\{\sigma(x)\mid\sigma\in A\}\) and \(\{\sigma(x)\mid\sigma\in B\}\) coincide. The quotient \({\mathcal B}(S_n)/ \sim\) is denoted by \({\mathcal F}P(S_n)\). It is proved that all automorphisms of the semigroup \({\mathcal F}P^+(S_n)={\mathcal F}P(S_n)\setminus\emptyset\) are inner.
scientific article; zbMATH DE number 1445566