A method of finding automorphism groups of endomorphism monoids of relational systems |
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Authors: | João Araújo Janusz Konieczny |
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Institution: | a Universidade Aberta, R. Escola Politécnica, 147, 1269-001 Lisboa, Portugal b Centro de Álgebra, Universidade de Lisboa, 1649-003 Lisboa, Portugal c Department of Mathematics, University of Mary Washington, Fredericksburg, VA 22401, USA |
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Abstract: | 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 NS(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 NS(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. |
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Keywords: | 20M20 20M15 05C25 05C65 |
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