Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Some complete sets of complementary elements of the symmetric and the alternating group of the n-th degree

Abstract

It is proved that some classes\(\mathfrak{H}\) of conjugate elements in a symmetric and in an alternating group are complete sets of complementing elements, i.e., subsets such that for each non-identity element A of the group there exists an element B ∉\(\mathfrak{H}\) such that A and B generate the group.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    N. G. Chebotarev, Foundations of Galois Theory [in Russian], Leningrad-Moscow (1934).

  2. 2.

    N. G. Chebotarev, Galois Theory [in Russian], Moscow-Leningrad (1936).

  3. 3.

    S. Piccard, “On the bases of the symmetric and the alternating group,” Math. Ann.,116, 752–769 (1939).

  4. 4.

    S. Piccard, On the Bases of the Symmetric Group and Pairs of Permutations which Generate a Regular Group, Paris (1946) (abbreviated Russian translation: Cybernetic Collection, No. 1, 7–34 (1965)).

  5. 5.

    R. Ball, “Maximal subgroups of a symmetric group,” Trans. Amer. Math. Soc.,121, No. 2, 393–407 (1966).

  6. 6.

    R. A. Bairamov, “Towards the problem of completeness in a symmetric semigroup of finite degree,” Diskretnyi Analiz, No. 8, 3–26 (1966).

  7. 7.

    G. Binder, On Embedding Elements of the Symmetric Group into a System of Generators Consisting of Two Elements [in Russian], Postgraduate Research Collection, Kazan' (1964), pp. 3–5.

Download references

Author information

Additional information

Translated from Matematicheskie Zametki, Vol. 7, No. 2, pp. 173–180, February, 1970.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Binder, G.Y. Some complete sets of complementary elements of the symmetric and the alternating group of the n-th degree. Mathematical Notes of the Academy of Sciences of the USSR 7, 105–109 (1970). https://doi.org/10.1007/BF01093491

Download citation

Keywords

  • Conjugate Element
  • Complementary Element