A method of finding automorphism groups of endomorphism monoids of relational systems

For any set X and any relation @r on X, let T(X,@r) be the semigroup of all maps a:X->X that preserve @r. Let S(X) be the symmetric group on X. If @r is reflexive, the group of automorphisms of T(X,@r) is isomorphic to N"S"("X")(T(X,@r)), the normalizer of T(X,@r) in S(X), that is, the group of permutations on X that preserve T(X,@r) under conjugation. The elements of N"S"("X")(T(X,@r)) have been described for the class of so-called dense relations @r. The paper is dedicated to applications of this result.

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