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Automorphism groups of centralizers of idempotents
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Orientador(es)
Resumo(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).
Descrição
Palavras-chave
Automorphism group Transformation semigroup Inner automorphism Centralizer Dempotent
Contexto Educativo
Citação
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