The large rank of a finite semigroup using prime subsets

The large rank of a finite semigroup (Gamma ) , denoted by (r_5(Gamma )) , is the least number (n) such that every subset of (Gamma ) with (n) elements generates (Gamma ) . Howie and Ribeiro showed that (r_5(Gamma ) = |V| + 1) , where (V) is a largest proper subsemigroup of (Gamma ) . This work considers the complementary concept of subsemigroups, called prime subsets, and gives an alternative approach to find the large rank of a finite semigroup. In this connection, the paper provides a shorter proof of Howie and Ribeiro’s result about the large rank of Brandt semigroups. Further, this work obtains the large rank of the semigroup of order-preserving singular selfmaps.