Article thumbnail

Groups that together with any transformation generate regular semigroups or idempotent generated semigroups

By João Araújo, James D. Mitchell and Schneider Csaba

Abstract

Let a be a non-invertible transformation of a finite set and let G be a group of permutations on that same set. Then 〈G,a〉∖G〈G,a〉∖G is a subsemigroup, consisting of all non-invertible transformations, in the semigroup generated by G and a . Likewise, the conjugates ag=g−1agag=g−1ag of a by elements of G generate a semigroup denoted by 〈ag|g∈G〉〈ag|g∈G〉. We classify the finite permutation groups G on a finite set X such that the semigroups 〈G,a〉〈G,a〉, 〈G,a〉∖G〈G,a〉∖G, and 〈ag|g∈G〉〈ag|g∈G〉 are regular for all transformations of X. We also classify the permutation groups G on a finite set X such that the semigroups 〈G,a〉∖G〈G,a〉∖G and 〈ag|g∈G〉〈ag|g∈G〉 are generated by their idempotents for all non-invertible transformations of X

Topics: Transformation semigroups, Idempotent generated semigroups, Regular semigroups, Permutation groups, Primitive groups, OʼNan–Scott Theorem
Publisher: 'Elsevier BV'
Year: 2011
DOI identifier: 10.1016/j.jalgebra.2011.07.002
OAI identifier: oai:repositorioaberto.uab.pt:10400.2/3799
Journal:

Suggested articles


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.