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- In mathematics, and in particular universal algebra, the concept of an n-ary group (also called n-group or multiary group) is a generalization of the concept of a group to a set G with an n-ary operation instead of a binary operation. By an n-ary operation is meant any 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 n = 2. The earliest work on these structures was done in 1904 by Kasner and in 1928 by Dörnte; 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. (en)
- Полиадическая группа (-арная группа) в общей алгебре — обобщение понятия группы, использующее -арную операцию вместо бинарной. Полиадические группы стали объектом самостоятельного изучения, начиная с работы В. Дёрнте. (ru)
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- In mathematics, and in particular universal algebra, the concept of an n-ary group (also called n-group or multiary group) is a generalization of the concept of a group to a set G with an n-ary operation instead of a binary operation. By an n-ary operation is meant any 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 n = 2. The earliest work on these structures was done in 1904 by Kasner and in 1928 by Dörnte; 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. (en)
- Полиадическая группа (-арная группа) в общей алгебре — обобщение понятия группы, использующее -арную операцию вместо бинарной. Полиадические группы стали объектом самостоятельного изучения, начиная с работы В. Дёрнте. (ru)
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- N-ary group (en)
- Полиадическая группа (ru)
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