Ana Paula Escada;
The PG-exponent of a pseudovariety of semigroups
C. J. Ash's proof of the ``Pointlike Conjecture" provides an algorithm to calculate the group-pointlike subsets of a finite semigroup S. We denote by P_G(S) the subsemigroup of P (S) whose elements are the group-pointlike subsets of S. This paper is concerned with some properties of the operator P_G which assigns to the pseudovariety V the pseudovariety P_GV generated by the semigroups P_G(S) with S in V . As P_G V is a subpseudovariety of P V , some of them come from properties of the power operator.
We show that P_G^3 V = \pv S for any pseudovariety of semigroups V that contains a semigroup such that the subsemigroup generated by its idempotents is non-permutative.