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

Araújo, João; Konieczny, Janusz

http://hdl.handle.net/10400.2/1991

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Authors

Araújo, João

Konieczny, Janusz

Abstract(s)

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

Keywords

Automorphism group Endomorphism Transformation semigroup Reflexive relation

URI

http://hdl.handle.net/10400.2/1991

Citation

Araújo, João; Konieczny, Janusz - A method of finding automorphism groups of endomorphism monoids of relational systems. "Discrete Mathematics" [Em linha]. ISSN 0012-365X. Vol. 307, nº 13 (June 2007), p. 1609-1620