Multiary quasigroup

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Definition

A multiary quasigroup or polyadic quasigroup is a n-ary quasigroup for some n \ge 2. Note that the n = 2 case corresponds to the usual notion of quasigroup.

A n-ary quasigroup is defined as a set G with a n-ary operation, i.e., a map f: G^n \to G such that the equation f(a_1,a_2,\dots,a_n) = b has a unique solution with any a_i as the unknown and all other quantities (i.e., all the other <mah>a_j</math>s and b) known.

Related notions