On the torsion in K2 of a field

For a field F, let G _n (F) = {{a,Φ _n (a)} ∈ K ₂(F) | a,Φ _n (a) ∈ F*}, where Φ _n (x) is the n-th cyclotomic polynomial. At first, by using Faltings’ theorem on Mordell conjecture it is proved that if F is a number field and if n ≠ 4, 8, 12 is a positive integer having a square factor then G _n (F) is not a subgroup of K ₂(F), and then by using the results of Manin, Grauert, Samuel and Li on Mordell conjecture theorem for function fields, a similar result is established for function fields over an algebraically closed field.