Group is n-ary group for all n

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Statement

Suppose G is a group where we denote the multiplication by concatenation (i.e., we omit the multiplication symbol). Let n be an integer with n \ge 2. We can equip G with the structure of a n-ary group (i.e., a multiary group for arity n) as follows: we define the n-ary operation f:G^n \to G as:

f(a_1,a_2,\dots,a_n) = a_1a_2 \dots a_n