details
Author(s)
Ana Paula Escada;
Title The PGexponent of a pseudovariety of semigroups
Abstract C. J. Ash's proof of the ``Pointlike Conjecture" provides an algorithm to calculate the grouppointlike subsets of a finite semigroup S. We denote by P_G(S) the subsemigroup of P (S) whose elements are the grouppointlike 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 nonpermutative.
Journal J. Algebra
Volume 223
Year 2000
Issue 1
Page(s) 1536
