The idempotent-separating degree of a block-group

Abstract

In this paper we describe the least non-negative integer n such that there exists an idempotent-separating homomorphism from a finite block-group S into the monoid of all partial transformations of a set with n elements. In particular, as for a fundamental semigroup S this number coincides with the smallest size of a set for which S can be faithfully represented by partial transformations, we obtain a generalization of Easdown’s result established for fundamental finite inverse semigroups.