Gal'mak A.M.
Remarks on polyadic groups

We prove that an n-ary semigroup (G,[ ]) is an n-ary group (n Ł 3) iff there exists d in G such that for every a, b from G and some fixed 1 Ł i,j Ł n-1 the following two equations
          [ aⁱ , b^n-i-1 , x ] = d and [ y , b^n-j-1 , a^j ] = b
are solvable.