Free Profinite Semigroups Over Some Classes of Semigroups Locally in D(G)

نویسنده

José Carlos Costa

چکیده

The theory of free profinite semigroups, which received its major impetus with the publication of Reiterman’s paper [17] in the early eighties, has proven to be an important tool in the study of pseudovarieties of semigroups and on the varieties of recognizable languages associated with them (via Eilenberg’s Theorem on varieties [13]). The importance of Reiterman’s theorem was immediately understood by Almeida [1, 2, etc] and Azevedo [10] who developed the theory. More recently, this approach has also received the attention of authors like Selmi, Trotter, Volkov, Weil, Zeitoun and others [7, 18, 22, 23, 25]. For a pseudovariety V, denote by LV the pseudovariety of all finite semigroups S such that eSe ∈ V for each idempotent e of S, and by DV the pseudovariety of all finite semigroups S in which each regular D-class is a subsemigroup of S which lies in V. Particularly important in this work are the pseudovarieties DReH, DRH and DLH, where, for a pseudovariety H of groups, ReH, RH and LH denote, respectively, the pseudovarieties of rectangular groups, of right groups and of left groups, all of whose subgroups lie in H. We recall that DReG is usually denoted by DO.

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