Endomorphisms and partial isomorphisms
Peter J. Cameron · Semigroup Forum · 2025
Let A be an algebra (in the sense of universal algebra). Define PISo(A) to be the inverse semigroup of partial isomorphisms of A, and End(A) the semigroup of endomorphisms of A. The purpose of this note is to record the following result. Theorem 1 Let A be a finite abelian group. Then |PIso(A)| = |End(A)|.