Automorphism groups of centralizers of idempotents

✍ Scribed by João Araújo; Janusz Konieczny

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 209 KB
• Volume: 269
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00499-x

✦ Synopsis

For a set X, an equivalence relation ρ on X, and a cross-section R of the partition X/ρ, consider the following subsemigroup of the semigroup T (X) of full transformations on X:

The semigroup T (X, ρ, R) is the centralizer of the idempotent transformation with kernel ρ and image R. We prove that the automorphisms of T (X, ρ, R) are the inner automorphisms induced by the units of T (X, ρ, R) and that the automorphism group of T (X, ρ, R) is isomorphic to the group of units of T (X, ρ, R).