Automorphism groups of centralizers of idempotents

Araújo, João; Konieczny, Janusz

http://hdl.handle.net/10400.2/3809

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Authors

Araújo, João

Konieczny, Janusz

Abstract(s)

For a set X, an equivalence relation Ω on X, and a cross-section R of the partition X/Ω, consider the following subsemigroup of the semigroup T(X) of full transformations on X:T(X, Ω,R) = {a 2 T(X) : Ra μ R and (x, y) 2 Ω ) (xa, ya) 2 Ω}. The semigroup T(X, Ω,R) is the centralizer of the idempotent transformation with kernel Ω and image R. We prove that the automorphisms of T(X, Ω,R) are the inner automorphisms induced by the units of T(X, Ω,R) and that the automorphism group of T(X, Ω,R) is isomorphic to the group of units of T(X, Ω,R).

Keywords

Automorphism group Transformation semigroup Inner automorphism Centralizer Dempotent

URI

http://hdl.handle.net/10400.2/3809

Citation

Araújo, João; Konieczny, Janusz - Automorphism groups of centralizers of idempotents. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 269, nº 1 (2003), p. 1-12