Around the Hosszú-Gluskin theorem for n-ary groups

  title={Around the Hossz{\'u}-Gluskin theorem for n-ary groups},
  author={Wieslaw A. Dudek and Kazimierz Glazek},
  journal={Discret. Math.},
  • W. Dudek, K. Glazek
  • Published 10 October 2005
  • Mathematics, Computer Science
  • Discret. Math.
We survey the results related to the important Hosszu-Gluskin Theorem on n-ary groups adding several new results and comments. The aim of this paper is to write all such results in uniform and compressive forms. Therefore some proofs of new results are only sketched or omitted if their completing seems to be not too difficult for readers. In particular, we show as the Hosszu-Gluskin Theorem can be used for evaluation how many different n-ary groups (up to isomorphism) exist on some small sets… 

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