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CENTRALIZERS IN THE SEMIGROUP OF INJECTIVE TRANSFORMATIONS ON AN INFINITE SET

Part of: Semigroups

Published online by Cambridge University Press:  22 June 2010

JANUSZ KONIECZNY
JANUSZ KONIECZNY*
Affiliation:
Department of Mathematics, University of Mary Washington, Fredericksburg, VA 22401, USA (email: jkoniecz@umw.edu)
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Abstract

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For an infinite set X, denote by Γ(X) the semigroup of all injective mappings from X to X. For α∈Γ(X), let C(α)={β∈Γ(X):αβ=βα} be the centralizer of α in Γ(X). For an arbitrary α∈Γ(X), we characterize the elements of C(α) and determine Green’s relations in C(α), including the partial orders of ℒ-, ℛ-, and 𝒥-classes.

Keywords

injective transformationscentralizersGreen’s relations

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 2 , October 2010 , pp. 305 - 321
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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