The large rank of a finite semigroup using prime subsets

Abstract

The large rank of a finite semigroup , denoted by r5( ), is the least number n such that every subset of with n elements generates . Howie and Ribeiro showed that r5( ) = |V| + 1, where V is a largest proper subsemigroup of . 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