Syntactic and Global Semigroup Theory: A Synthesis Approach

  • Jorge Almeida
  • Benjamin Steinberg
Conference paper
Part of the Trends in Mathematics book series (TM)


This paper is the culmination of a series of work integrating syntactic and global semigroup theoretical approaches for the purpose of calculating semidirect products of pseudovarieties of semigroups. We introduce various abstract and algorithmic properties that a pseudovariety of semigroups might possibly satisfy. The main theorem states that given a finite collection of pseudovarieties, each satisfying certain properties of the sort alluded to above, any iterated semidirect product of these pseudovarieties is decidable. In particular, the pseudovariety G of finite groups satisfies these properties. J. Rhodes has announced a proof, in collaboration with J. McCammond, that the pseudovariety A of finite aperiodic semigroups satisfies these properties as well. Thus, our main theorem would imply the decidability of the complexity of a finite semigroup. Their work, in light of our main theorem, would imply the decidability of the complexity of a finite semigroup.


Word Problem Cayley Graph Semidirect Product Semi Direct Product Finite Semigroup 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Jorge Almeida
    • 1
  • Benjamin Steinberg
    • 2
  1. 1.Faculdade de CiênciasUniversidade do Porto P. Gomes TeixeiraPortoPortugal
  2. 2.Department of MathematicsUniversity of PortoPortoPortugal

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