A method of finding automorphism groups of endomorphism monoids of relational systems - Araújo, João (2011)
For any set X and any relation ρ on X, let T(X,ρ) be the semigroup of all maps a : X → X that preserve ρ. Let S(X) be the symmetric group on X. If ρ is reflexive, the group of automorphisms of T (X, ρ) is isomorphic to N_{S(X)}(T (X, ρ)), the normalizer of T (X, ρ) in S(X), that is, the group of permutations on X that preserve T (X, ρ) under conjugation. The elements of N_{S(X)}(T (X, ρ)) have been described for the class of so-called dense relations ρ. The paper is dedicated to applications of this result. © 2006 Elsevier B.V. All rights reserved.