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A construction of the free digroup

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Abstract

We give a construction of the free digroup on a set X and describe the halo and the group parts of it. We prove that the free digroup on X is isomorphic to the free digroup on a set Y if and only if \(card(X)=card(Y)\).

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Acknowledgements

We wish to express our thanks to the referee for helpful suggestions and comments.

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Authors and Affiliations

  1. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510631, People’s Republic of China

    Guangliang Zhang

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Yuqun Chen

Authors
  1. Guangliang Zhang
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  2. Yuqun Chen
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Correspondence to Yuqun Chen.

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Communicated by Mikhail Volkov.

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Supported by the NNSF of China (11571121,12071156)

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Zhang, G., Chen, Y. A construction of the free digroup. Semigroup Forum 102, 553–567 (2021). https://doi.org/10.1007/s00233-021-10161-6

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  • DOI: https://doi.org/10.1007/s00233-021-10161-6

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