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An Alternative Method for Construction of Free Polyadic Groups

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Abstract

In this article, we introduce a new method to constructing free polyadic groups which is more natural than the previous one given in Khodabandeh and Shahryari (Commun Algebra 45(3): 1227–1238, 2017). This new approach is a natural generalization of the construction of ordinary free groups as sets of reduced group words.

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References

  1. Artamonov, V.: Free \(n\)-groups. Matematicheskie Zametki 8, 499–507 (1970)

    MathSciNet  Google Scholar 

  2. Artamonov, V.: On Schreier varieties of \(n\)-groups and \(n\)-semigroups. Trudy Seminara Imeni I.G. Petrovskogo 5, 193–203 (1979)

    MathSciNet  MATH  Google Scholar 

  3. Dörnte, W.: Unterschungen über einen verallgemeinerten Gruppenbegriff. Math. Z. 29, 1–19 (1929)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dudek, W.: Varieties of polyadic groups. Filomat 9, 657–674 (1995)

    MathSciNet  MATH  Google Scholar 

  5. Dudek, W.: Remarks on \(n\)-groups. Demonstr. Math. 13, 65–181 (1980)

    MathSciNet  MATH  Google Scholar 

  6. Dudek, W., Glazek, K.: Around the Hosszú–Gluskin theorem for n-ary groups. Discrete Math. 308, 4861–4876 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dudek, W., Michalski, J.: On a generalization of Hosszú theorem. Demonstr. Math. 15, 437–441 (1982)

    MATH  Google Scholar 

  8. Dudek, W., Michalski, J.: On retract of polyadic groups. Demonstr. Math. 17, 281–301 (1984)

    MathSciNet  MATH  Google Scholar 

  9. Dudek, W., Shahryari, M.: Representation theory of polyadic groups. Algebra Represent Theory 15, 29–51 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Galmak, A.: N-ary groups. Gomel University Press, Gomel (2003)

    Google Scholar 

  11. Galmak, A.: Remarks on polyadic groups. Quasigroups Relat. Syst. 7, 67–70 (2000)

    MathSciNet  Google Scholar 

  12. Gleichgewicht, B., Glazek, K.: Remarks on n-groups as abstract algebras. Colloq. Math. 17, 209–219 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hosszú, M.: On the explicit form of \(n\)-groups. Publ. Math. 10, 88–92 (1963)

    MathSciNet  MATH  Google Scholar 

  14. Kasner, E.: An extension of the group concept. Bull. Am. Math. Soc. 10, 290–291 (1904)

    MATH  Google Scholar 

  15. Khodabandeh, H., Shahryari, M.: On the representations and automorphisms of polyadic groups. Commun. Algebra 40, 2199–2212 (2012)

    Article  MATH  Google Scholar 

  16. Khodabandeh, H., Shahryari, M.: Simple polyadic groups. Sib. Math. J. 55, 734–744 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Khodabandeh, H., Shahryari, M.: Equations in polyadic groups. Commun. Algebra 45(3), 1227–1238 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Post, E.: Polyadic groups. Trans. Am. Math. Soc. 48, 208–350 (1940)

    Article  MathSciNet  MATH  Google Scholar 

  19. Shahryari, M.: Representations of finite polyadic groups. Commun. Algebra 40, 1625–1631 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Sokolov, E.: On the Gluskin–Hosszú theorem for Dornte \(n\)-groups. Istor. -Mat. Issled 39, 187–189 (1976)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    Elnaz Nobahar, Mehrdad Azadi & Hossein Doostie

Authors
  1. Elnaz Nobahar
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  2. Mehrdad Azadi
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  3. Hossein Doostie
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Corresponding author

Correspondence to Mehrdad Azadi.

Additional information

Communicated by Hamid Mousavi.

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Nobahar, E., Azadi, M. & Doostie, H. An Alternative Method for Construction of Free Polyadic Groups. Bull. Iran. Math. Soc. 45, 401–410 (2019). https://doi.org/10.1007/s41980-018-0139-1

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  • DOI: https://doi.org/10.1007/s41980-018-0139-1

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