Araújo, JoãoMitchell, James D.Csaba, Schneider2015-03-232015-03-232011Araújo, João; Mitchell, James D.; Schneider, Csaba - Groups that together with any transformation generate regular semigroups or idempotent generated semigroups. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 343, nº 1 (2011), p. 1-160021-8693http://hdl.handle.net/10400.2/3799Let 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.engTransformation semigroupsIdempotent generated semigroupsRegular semigroupsPermutation groupsPrimitive groupsOʼNan–Scott Theoremjournal articledoi:10.1016/j.jalgebra.2011.07.002