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Infinite injective transformations whose centralizers have simple structure

Janusz Konieczny — 2011

Open Mathematics

For an infinite set X, denote by Γ(X) the semigroup of all injective mappings from X to X under function composition. For α ∈ Γ(X), let C(α) = β ∈ g/g(X): αβ = βα be the centralizer of α in Γ(X). The aim of this paper is to determine those elements of Γ(X) whose centralizers have simple structure. We find α ∈ (X) such that various Green’s relations in C(α) coincide, characterize α ∈ Γ(X) such that the 𝒥 -classes of C(α) form a chain, and describe Green’s relations in C(α) for α with so-called finite...

Second centralizers of partial transformations

Janusz Konieczny — 2001

Czechoslovak Mathematical Journal

Second centralizers of partial transformations on a finite set are determined. In particular, it is shown that the second centralizer of any partial transformation α consists of partial transformations that are locally powers of α .

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