n-Groups derivable from groups

The trivial extentions of binary operation ∗ to the n-ary operation ϕ has the form ϕ(x1, x2, . . . , xn) = x1 ∗ x2 ∗ · · · ∗ xn ∗ a. If (G, ∗) is a group and a ∈ Z(G, ∗) the center of (G, ∗) then (G, ϕ) is an n-group so called n-group derived from (G, ∗). It is known that there exist n-groups (G, ϕ) which cannot be obtained as a derived group. The goal of the paper is to characterize all the n-groups operations which are derivable from group operations.