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On two classes of digroups

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Abstract

The paper is devoted to studying two classes of digroups. We give new examples of digroups of such classes and construct an abelian digroup for which any mapping of its generating set to an arbitrary abelian digroup with one bar-unit can be uniquely extended to a homomorphism of these digroups. We also describe a congruence on a free dimonoid for which the quotient is an abelian digroup construction mentioned above.

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References

  1. Loday, J.-L.: Dialgebras, Dialgebras and related operads: Lect. Notes Math., vol. 1763, pp. 7–66. Springer, Berlin (2001)

  2. Zhuchok, A.V.: Free commutative dimonoids. Algebra Discrete Math. 9(1), 109–119 (2010)

    MathSciNet  MATH  Google Scholar 

  3. Zhuchok, A.V.: Free \(n\)-nilpotent dimonoids. Algebra Discrete Math. 16(2), 299–310 (2013)

    MathSciNet  MATH  Google Scholar 

  4. Zhuchok, A.V., Zhuchok, Yul.V.: Free left \(n\)-dinilpotent dimonoids. Semigroup Forum (2015). doi:10.1007/s00233-015-9743-z

  5. Zhuchok, Y.V.: Representations of ordered dimonoids by binary relations. Asian Eur. J. Math. 07, 1450006-1–1450006-13 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kinyon, M.K.: Leibniz algebras, Lie racks, and digroups. J. Lie Theory 17(1), 99–114 (2007)

    MathSciNet  MATH  Google Scholar 

  7. Felipe, R.: Generalized Loday algebras and digroups (2004). Comunicaciones del CIMAT, No. I-04-01/21-01-2004

  8. Liu, K.: Transformation digroups, Preprint available at arXiv:math.GR/0409265 (2004)

  9. Liu, K.: The generalizations of groups. Res. Monogr. Math. Publ. Burnaby 1, 153 (2004)

    Google Scholar 

  10. Phillips, J.D.: A short basis for the variety of digroups. Semigroup Forum 70, 466–470 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhuchok, Yu.V.: Endomorphisms of free abelian monogenic digroups. Mat. Stud. 43(2), 144–152 (2015)

  12. Zhuchok, A.V.: Dimonoids and bar-units. Siberian Math. J. 56(5), 827–840 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The authors express their deep gratitude to the referee for helpful advices, suggestions and comments.

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Authors and Affiliations

  1. Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Gogol Square, 1, Starobilsk, 92703, Ukraine

    Anatolii Zhuchok

  2. Department of Geometry, Kyiv Taras Shevchenko National University, Volodymyrska Street, 60, Kyiv, 01033, Ukraine

    Yurii Zhuchok

Authors
  1. Anatolii Zhuchok
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  2. Yurii Zhuchok
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Correspondence to Yurii Zhuchok.

Additional information

Anatolii Zhuchok was supported by SAIA (The National Scholarship Programme of the Slovak Republic).

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Zhuchok, A., Zhuchok, Y. On two classes of digroups. São Paulo J. Math. Sci. 11, 240–252 (2017). https://doi.org/10.1007/s40863-016-0038-4

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