Abstract
Ash's proof of the Pointlike Conjecture provides an algorithm for calculating the group-pointlike subsets of a finite semigroup S. We denote by PG(S) the subsemigroup of P(S), the elements of which are the group-pointlike subsets of S. This paper is concerned with some properties of the operator PG, which assigns to the pseudovariety V the pseudovariety PGV generated by the semigroups PG(S) with S in V. As PGV is a subpseudovariety of PV, some of them come from properties of the power operator. We show that P3GV=S for any pseudovariety of semigroups V that contains a semigroup such that the subsemigroup generated by its idempotents is non-permutative.
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