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On Identities and m-Neutral Sequences of n-Ary Groups

Abstract

In this paper, we study such polyadic analog of an identity of a group as m-neutral sequence. In particular, we prove that all Post’s equivalence classes of the free covering group of any n-ary group [where \(n = k(m - 1) + 1\) and \(k\ge 1\)] defined by m-neutral sequences form the \((k + 1)\)-ary group, which is isomorphic to the n-ary subgroup of all identities of the n-ary group in the case when \(m = 2\).

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References

  1. 1.

    Gal’mak, A.M.: The \(n\)-Ary Subgroup of Identities, pp. 1–23. Francisk Skorina Gomel State University, Gomel (2003)

    Google Scholar 

  2. 2.

    Gal’mak, A.M.: \(n\)-Ary Groups. Belarusian State University, Minsk (2007)

    MATH  Google Scholar 

  3. 3.

    Gal’mak, A.M.: On identities of an \(n\)-ary group. Asian Eur. J. Math. 9(2), 43–51 (2016)

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Gal’mak, A.M.: \(n\)-Ary Groups. Francisk Skorina Gomel State University, Gomel (2003)

    MATH  Google Scholar 

  5. 5.

    Rusakov, S.A.: Algebraic \(n\)-Ary Systems. Navuka i thechnica, Minsk (1992)

    Google Scholar 

  6. 6.

    Dörnte, W.: Untersuchungen über einen verallgemeinerten Gruppenbegrieff. Math. Z 29, 1–19 (1928)

    Article  MATH  Google Scholar 

  7. 7.

    Post, E.L.: Polyadic groups. Trans. Am. Math. Soc. 48(2), 208–350 (1940)

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Tjutin, V.I.: To axiomatics of \(n\)-ary groups. Dokl. Akad. Nauk. BSSR 29(8), 691–693 (1985)

    MathSciNet  Google Scholar 

  9. 9.

    Gal’mak, A.M., Shchuchkin, N.A.: To the Post’s coset theorem. Chebyshevsky sbornik 15(2), 6–20 (2014)

    MathSciNet  Google Scholar 

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Correspondence to Viktoria A. Kovaleva.

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Gal’mak, A.M., Kovaleva, V.A. On Identities and m-Neutral Sequences of n-Ary Groups. Commun. Math. Stat. 4, 495–508 (2016). https://doi.org/10.1007/s40304-016-0097-y

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Keywords

  • n-Ary group
  • Identity
  • m-Neutral sequence

Mathematics Subject Classification

  • 20N15