On Some Elements Of Finite Order In K₂Q

In this paper, we first investigate Gn(Q) where n has two or three prime factors. We discuss the discrete valuation of @n(a, b) correspording to the prime factors of n. Then we give the necessary Diophantine equation when Gn(Q) is a subgroup of K2Q. Then we use these results to prove that none of G15(Q),Gn(Q),G33(Q),G35(Q),G55(Q),G60(Q),G1O5(Q) is a subgroup of K2Q by computing. Thus we partially verify Browkin's conjecture. At last, we discuss the necessary Diophantine equations about (a, b) when Gn(Q) is a group where n = conjecture to end this paper.