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

Joao Araujo, J. D. Mitchell, Csaba Schneider

Let $a$ be a non-invertible transformation of a finite set and let $G$ be a group of permutations on that same set. Then $\genset{G, a}\setminus G$ is a subsemigroup, consisting of…