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; 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.