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Finite subgroups of ∨-semilatticed inverse semigroups

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Abstract

In this paper we describe the ∨-semilatticed inverse semigroups generated by a finite group G. We do this by first constructing the free ∨-semilatticed inverse semigroup ℱ(G) on the group G. Each ∨-semilatticed inverse semigroup generated by G is a quotient of ℱ(G) by a ∨-congruence. We then describe these congruences and their corresponding quotients explicitly in terms of families of subgroups of G.

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Authors and Affiliations

  1. Centro de Álgebra da Universidade de Lisboa (CAUL), Av. Prof. Gama Pinto 2, 1495-002, Lisbon, Portugal

    A. Paula Garrão & Donald B. McAlister

  2. Universidade dos Açores, Apartado 1422, 9501-801, Ponta Delgada, Portugal

    A. Paula Garrão

  3. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115, USA

    Donald B. McAlister

Authors
  1. A. Paula Garrão
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  2. Donald B. McAlister
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Corresponding author

Correspondence to A. Paula Garrão.

Additional information

Communicated by László Márki.

This work was partially financed by Fundação Luso-Americana para o Desenvolvimento (FLAD) within the project 87/99 and developed within the projects POCTI/MAT/32440/2000 “Álgebra e Aplicações” and POCTI-ISFL-1-143 “Álgebra Fundamental e Aplicada” of Centro de Álgebra da Universidade de Lisboa, financed by FCT and FEDER. The second author is also supported by FLAD under grant 071/2008.

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Garrão, A.P., McAlister, D.B. Finite subgroups of ∨-semilatticed inverse semigroups. Semigroup Forum 78, 187–199 (2009). https://doi.org/10.1007/s00233-008-9092-2

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  • DOI: https://doi.org/10.1007/s00233-008-9092-2

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