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N-ary group : ウィキペディア英語版
N-ary group

In mathematics, and in particular universal algebra, the concept of ''n''-ary group (also called ''n''-group or multiary group) is a generalization of the concept of group to a set ''G'' with an ''n''-ary operation instead of a binary operation.〔.〕 By an ''n''-ary operation is meant any set map ''f: Gn → G'' from the ''n''-th Cartesian power of ''G'' to ''G''. The axioms for an ''n''-ary group are defined in such a way that they reduce to those of a group in the case . The earliest work on these structures was done in 1904 by Kasner and in 1928 by Dörnte;〔W. Dörnte, Untersuchungen über einen verallgemeinerten Gruppenbegriff, ''Mathematische Zeitschrift'', vol. 29 (1928), pp. 1-19.〕 the first systematic account of (what were then called) polyadic groups was given in 1940 by Emil Leon Post in a famous 143-page paper in the ''Transactions of the American Mathematical Society''.〔E. L. Post, (Polyadic groups ), ''Transactions of the American Mathematical Society'' 48 (1940), 208–350.〕
==Axioms==


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