Permutations of a semigroup that map to inverses.
Let \(PT_X\) be the partial transformation semigroup on the set \(X\), \(V(u)\) the set of inverses of \(u\in PT_X\). For a semigroup \(S\) a permutation \(f\) on \(S\) is called permutation matching, if \(f\in PT_S\) and \(f(a)\in V(a)\) for every \(a\in\text{dom\,}f\). It is shown that the finite full transformation semigroup has a permutation matching.
scientific article; zbMATH DE number 6363664