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General Theorems on Automorphisms of Semigroups and Their Applications

Araújo, João; Konieczny, Janusz

Journal of the Australian Mathematical Society, 87(1) (2009), 1-17

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.