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n-ary quasi-groups and loops

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Literature Cited

  1. W. Dörnte, “Investigation into a generalized group concept” [in German], Math. Zeits.,29 (1928), pp. 1–19.

    Google Scholar 

  2. A. K. Sushkevich, Theory of Generalized Groups [in Russian], Gos. nauchn. tekhn. izd., Kharkov-Kiev (1937).

    Google Scholar 

  3. G. Chupona, “Finitary operation” [in Serbian], Godishen. zb. prirodno-matem. fak. un-t Skopje,12, No. 11 (1959-(1961), pp. 7–49.

    Google Scholar 

  4. G. Chupona, “N-ary sub-semi-groups” [in Serbian], Bilten. Drinet. matem. i fiz.,12 (1961), pp. 5–13.

    Google Scholar 

  5. B. Trepenovski and G. Chupona, “Finitary associative operations with neutral elements” [in Serbian], Bilten. Drusht. matem. i fiz.,12 (1961), pp. 15–24.

    Google Scholar 

  6. R. M. Dicker, The substitutive law, Proc. London Math. Soc.,13, No. 3 (1963), pp. 493–510.

    Google Scholar 

  7. F. Rado, Generalizarea tesuturilor spatiale pentru structuri algebrice, Studia Univ. Babes-Bolyai, Math.-Phys., No. 1 (1960), pp. 41–55.

    Google Scholar 

  8. M. Hosszu and F. Rado, “A class of ternary quasi-groups” [in German], Acta Math. Hung,15, Nos. 1, 2 (1964), pp. 29–36.

    Google Scholar 

  9. S. A. Chunikhin, “Theory of non-associative n-groups with postulate K,” Doklady Ak. nauk SSSR,48, (1945), pp. 7–10.

    Google Scholar 

  10. A. G. Kurosh, Lectures on Higher Algebra [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  11. A. I. Mal'tsev, “Towards a general theory of algebraic systems,” Matem. sb.,35, No. 1 (1954), pp. 3–20.

    Google Scholar 

  12. V. D. Belousov, “Regular substitutions in quasi-groups,” Uch. zap. Bel'tsskogo ped. in-ta,1 (1958), pp. 39–49.

    Google Scholar 

  13. A. A. Albert, Quasigroups, I, Trans. Amer. Math. Soc., 54, No. 2 (1943), pp. 507–519.

    Google Scholar 

  14. M. D. Sandik, “Units in n-loops. Investigations in algebra and in mathematical analysis,” Ak. nauk MoldSSR (1965), pp. 140–146.

  15. H. Minc, Index polynomials and bifurcating root-trees, Proc. Royal. Soc., Edinburgh,64, No. 4 (1956–1957), pp. 319–341.

    Google Scholar 

  16. M. Hosszu, On the explicit form of n-group operations, Publ. math., 10, No. 1-4 (1963), pp. 88–92.

    Google Scholar 

  17. L. M. Gluskin, “On positional operators,” Doklady Ak. nauk SSSR,157, No. 4 (1964), pp. 767–770.

    Google Scholar 

  18. H. B. Mann, The construction of orthogonal Latin squares, Ann. Math. Statistics, 13 (1942), pp. 418–423.

    Google Scholar 

  19. V. D. Belousov and M. Hosszu, Some problems on ternary quasi-groups, Publ. Math. Debrecen, 12 (1965).

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Authors
  1. V. D. Belousov
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  2. M. D. Sandik
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 7, No. 1, pp. 31–54, January–February, 1966

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Belousov, V.D., Sandik, M.D. n-ary quasi-groups and loops. Sib Math J 7, 24–42 (1966). https://doi.org/10.1007/BF00967815

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