Neither G_9(Q) nor G_(11)(Q) Is a Subgroup of K_2(Q)

It is proved that neither G9(Q) nor G11(Q) is a subgroup of K2(Q)which confirms two special cases of a conjecture proposed by Browkin, J. (LectureNotes in Math., 966, Springer-Verlag, New York, Heidelberg, Berlin, 1982, 1-6).

K_2■ 的某些有限阶元素

本文证明了若ｎ≥２，则Ｇ２ｎ３ｍ（■）是Ｋ_２■Ｑ的子群当且仅当ｎ＝２，ｍ＝０；并且通过改进［１］的方法，还证明了Ｇ２５（■），Ｇ４９（■）和Ｇ２７（■）都不是Ｋ_２■的子群，从而部分地证实了Ｂｒｏｗｋｉｎ的一个著名猜想．

G_3n^n(Q)(n≥3)不是K_2Q的子群

设Φn(x) 是 n 次分圆多项式,记 Gn(F) = {{x,Φn(x)} ∈ K2F x,Φn(x) ∈F*},其中F是域.证明了当n≥3时,G3n (Q)不是K2 Q的子群,从而部分地证实了Browkin 的一个猜想.

K_2Q中的有限阶元

通过对丢番图方程的研究,给出G10(Q)是K2Q的子群时必须要满足的丢番图方程,然后根据所得结论证明了G(Q),G(Q)都不是KQ的子群,从而部分证明了Browkin的一个猜想.

A conjecture on a class of elements of finite order in K_2F_■

For a local field F the finite subgroups of K2F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a conjecture posed by Browkin.