General Theorems on Automorphisms of Semigroups and Their Applications

Journal of the Australian Mathematical Society, 87(1) (2009), 1-17
http://dx.doi.org/10.1017/S1446788709000019

We introduce the notion of a strong representation of a semigroup in the monoid of endomorphisms of any mathematical structure, and use this concept to provide a theoretical description of the automorphism group of any semigroup. As an application of our general theorems, we extend to semigroups a well-known result concerning automorphisms of groups, and we determine the automorphism groups of certain transformation semigroups and of the fundamental inverse semigroups.