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.