A new construction for free inverse semigroups (Q790947)

If X is any non-empty set we denote the free group on X by G(X) and the symmetric inverse semigroup (under composition) of partial one-to-one transformations of G(X) by \({\mathcal I}_{G(X)}\). In this paper the free inverse semigroup \(I_ X\) on X is constructed as a certain inverse subsemigroup of \({\mathcal I}_{G(X)}\). The elements of \(I_ X\) are partial transformations of G(X) which are particularly simple to describe.