High Quality Content by WIKIPEDIA articles! In mathematics, an n-ary group (also n-group, polyadic group or multiary group) is a generalization of a group to a set G with a n-ary operation instead of a binary operation. The axioms for an n-ary group are defined in such a way as to reduce to those of a group in the case n = 2.The easiest axiom to generalize is the associative law. Ternary associativity is (abc)de = a(bcd)e = ab(cde), i.e. the string abcde with any three adjacent elements bracketed. n-ary associativity is a string of length n+(n-1) with any n adjacent elements bracketed. A set G with a closed n-ary operation is an n-ary groupoid. If the operation is associative then it is an n-ary semigroup.

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