2005/10/10 by Wieslaw A. Dudek, Wiesław A. Dudek, Kazimierz Glazek +1 · 4 citations
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research #Nonlinear Differential Equations Analysis #math.GM #math.GR #msc:20N15
paper · pdf · doi:10.1016/j.disc.2007.09.005
published as Discrete Mathematics 308 (2008), 4861-4876
arxiv created 2005/10/10 · openalex publication_date 2007/12/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02
We survey results related to the important Hosszú-Gluskin Theorem on n-ary groups adding also 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 Hosszú-Gluskin Theorem can be used for evaluation how many different n-ary groups (up to isomorphism) exist on some small sets. Moreover, we sketch as the mentioned theorem can be also used for investigation of Q-independent subsets of semiabelian n-ary groups for some special families Q of mappings.