University of Nis, Serbia
Semigroups generated by a group and an idempotent
It is well known that the full transformation semigroup on a finite set with n elements is generated by its group of units, the symmetric group, and any idempotent of rank n-1. In this talk we shall give some results on the structure of a semigroup generated by a group of permutations on a set with n elements and an idempotent of rank n-1. All such semigoups are regular and,in the case when the group is generated by a cycle of length n, or is dihederal, they exhibit some pleasant combinatorial properties. We will also describe some recent results of J. André for the case when the added generator need not be idempotent.