Open multiplication in relatively free profinite semigroupoids
Jorge Almeida, Alfredo Costa, Herman Goulet-Ouellet
TL;DR
This paper extends the openness of multiplication from finitely generated free profinite semigroups to semigroupoids over finite graphs, providing new insights into recurrent words and stabilizers in these structures.
Contribution
It introduces the concept of open multiplication in relatively free profinite semigroupoids and applies it to characterize recurrent words and analyze stabilizers.
Findings
Multiplication is open in relatively free profinite semigroupoids.
Provides a profinite characterization of recurrent words over infinite alphabets.
Establishes new results on stabilizers in profinite semigroups and semigroupoids.
Abstract
The purpose of this paper is to extend some useful results, such as the multiplication being open, previously known for suitable finitely generated relatively free profinite semigroups, to relatively free profinite semigroupoids over finite-vertex graphs. This extension is used to give a profinite characterization of recurrent words over infinite alphabets and to establish new results about stabilizers in relatively free profinite semigroups and semigroupoids.
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