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Abelian and symmetric generalized digroups

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Abstract

In this paper we extend some group-like concepts to generalized digroups. We exhibit examples of non-abelian cyclic generalized digroups. We show that abelian generalized digroups are tightly related to left commutative semigroups with left identities and right inverses, and characterize these semigroups using generalized digroups properties. We also present symmetric generalized digroups and the transformation generalized digroup.

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Acknowledgements

We thank the referee for the valuable comments. The first two authors want to thank the Project Hermes Code 45519. The third author acknowledges to Vicerrectoría de Investigaciones, Universidad de Antioquia, and was supported under CIEN research project Sobre el segundo grupo de cohomología en superálgebras de Jordan Code 2019-26870.

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Authors and Affiliations

  1. Escuela de Matemáticas, Universidad Nacional de Colombia, Medellín, Colombia

    José Gregorio Rodríguez-Nieto & Olga P. Salazar-Díaz

  2. Instituto de Matemáticas, Universidad de Antioquia, Medellín, Colombia

    Raúl Velásquez

Authors
  1. José Gregorio Rodríguez-Nieto
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  2. Olga P. Salazar-Díaz
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  3. Raúl Velásquez
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Corresponding author

Correspondence to Raúl Velásquez.

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Communicated by Mikhail Volkov.

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Rodríguez-Nieto, J.G., Salazar-Díaz, O.P. & Velásquez, R. Abelian and symmetric generalized digroups. Semigroup Forum 102, 861–884 (2021). https://doi.org/10.1007/s00233-021-10162-5

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  • DOI: https://doi.org/10.1007/s00233-021-10162-5

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