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