Automorphisms of partial endomorphism semigroups

• Autor(a) principal: Araújo, João
• Data de Publicação: 2011
• Outros Autores: Fernandes, Vítor H., Jesus, Manuel M., Maltcev, V., Mitchell, James D.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.2/3808
• topic: Automorphisms; Endomorphism semigroups; Relations

In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures with a single m-ary relation for any m 2 N over a finite set. We use this recipe to determine the automorphism groups of the following semigroups:the full transformation semigroup, the partial transformation semigroup, and the symmetric inverse semigroup, and their wreath products, partial endomorphisms of partially ordered sets, the full spectrum of semigroups of partial mappings preserving or reversing a linear or circular order. We also determine the automorphism groups of the so-called Madhaven semigroups as an application of the methods developed herein.