The Finite Field On Function Field K < Sub > 2 < / Sub > Group Of Torsion

Let K2(F) be the Milnor K2-group of a field F, andΦn(x) the n-th cy-clotomic polynomial. Denote Gn(F)={{a,Φn(a)}∈K2(F)|a,Φn(a)∈F*}. Browkin proved in 1980s that for any field F≠F2 and n=1,2,3,4,or 6, Gn(F) is a subgroup of K2(F). He also gave a conjecture that for n≠1,2,3,4,6, Gn(F) is not a subgroup of K2(F).In the present paper, we investigate the case of F being the functional field over a finite field, and prove that neither G5(F2(x)) is a subgroup of K2(F2(x)) nor G5(F3(x)) a subgroup of K2(F3(x)).