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The main result of this paper is a proof of the fact that if is a -operative (i.e. an -ary operation on a set satisfying the identities where and are permutations, , , and , and if contains a two-sided invertible element (i.e. ), then a semigroup operation can be defined on such that for some invertible element of the semigroup and certain of its automorphisms or inverse automorphisms for which .Bibliography: 13 items.

In this paper the theorem on the representation of partially conjugate associative n-ary operations by binary and unary operations is proved.