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Semigroup presentations for test local groups

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Abstract

In this paper we exhibit a type of semigroup presentation which determines a class of local groups. We show that the finite elements of this class generate the pseudovariety \(\mathbf{LG}\) of all finite local groups and use them as test-semigroups to prove that \(\mathbf{LG}\) and \(\mathbf{S}\), the pseudovariety of all finite semigroups, verify the same \(\kappa \)-identities involving \(\kappa \)-terms of rank at most 1, where \(\kappa \) denotes the implicit signature consisting of the multiplication and the \((\omega -1)\)-power.

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Acknowledgments

This work was supported by the European Regional Development Fund, through the programme COMPETE, and by the Portuguese Government through FCT – Fundação para a Ciência e a Tecnologia, under the Project PEst-C/MAT/UI0013/2011.

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Authors and Affiliations

  1. CMAT, Departamento de Matemática e Aplicações, Universidade do Minho, Campus de Gualtar, 4700-320, Braga, Portugal

    J. C. Costa & M. L. Teixeira

  2. CMAT, Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Leiria, Campus 2, Morro do Lena, Alto Vieiro, 2411-901, Leiria, Portugal

    C. Nogueira

Authors
  1. J. C. Costa
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  2. C. Nogueira
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  3. M. L. Teixeira
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Correspondence to J. C. Costa.

Additional information

Communicated by Jorge Almeida.

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Costa, J.C., Nogueira, C. & Teixeira, M.L. Semigroup presentations for test local groups. Semigroup Forum 90, 731–752 (2015). https://doi.org/10.1007/s00233-014-9656-2

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  • DOI: https://doi.org/10.1007/s00233-014-9656-2

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