Algebra, Logic and Topology

 

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Author(s)
Ana Paula Escada;

Title
The PG-exponent of a pseudovariety of semigroups

Abstract
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.

Journal
J. Algebra

Volume
223

Year
2000

Issue
1

Page(s)
15-36

 
     
 

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