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Formations of inverse semigroups

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Abstract

This article explores a generalisation of the theory of formations of groups. Taking formations of groups as the starting point, formations of inverse semigroups are defined, as well as the wider classes of i-formations (i standing for idempotent-separating) and some classes of the kind named f-formations (f standing for fundamental). The relation between the nature of a class of groups and that of certain classes of inverse semigroups with associated groups in the first is discussed. The product of formations is considered, and a product like the Gaschütz’s product known for groups is presented for f-formations.

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Acknowledgements

This work was developed within the activities of Centro de Matemática Computacional e Estocástica, CEMAT, and Departamento de Matemática da Faculdade de Ciências da Universidade de Lisboa, within the projects UIDB/04621/2020, UIDP/04621/2020, UID/MULTI/04621/2019 and PTDC/MAT- PUR/31174/2017, financed by Fundação para a Ciência e a Tecnologia, FCT. The authors would like to thank Mário J. J. Branco and Mark V. Lawson for the pertinent discussions and suggestions. Thanks are also due to Pedro V. Silva for providing Example 4.5.

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Authors and Affiliations

  1. Faculdade de Ciências, Departamento de Matemática, Universidade de Lisboa, 1749-016, Lisboa, Portugal

    Gracinda M. S. Gomes

  2. NOVA School of Science and Technology, Department of Environmental Sciences and Engineering, 2825-149, Caparica, Portugal

    Isabel J. Nobre

Authors
  1. Gracinda M. S. Gomes
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  2. Isabel J. Nobre
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Correspondence to Gracinda M. S. Gomes.

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Communicated by Victoria Gould.

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Gomes, G.M.S., Nobre, I.J. Formations of inverse semigroups. Semigroup Forum 105, 217–243 (2022). https://doi.org/10.1007/s00233-022-10290-6

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