Abstract:
Formanek constructed the first central polynomial. i .e. G
1+ G
2+… + G
n where G
1= G(x, y
1,…, y
n), G
2= G(x, y
2, y
3,…, y
n, y
1) etc. Are called Forma nek's polynomials. Rosset in his nota 3 raised the question that whether all sgmmetic polynomials in G
i also give central polynomials. He showed that the basic sgmmetric polynomials in G
i are not all central. In this paper we shall show, for n≥3 each polynomial in G
j is not central, except f(G
1+ …+ G
n, where f(x)is a polynomial at x. Hence Formanek's central polynomial is unique in some sense.