G_(55)(Q)不是K_2Q的子群

G_(55)(Q) is not a subgroup of K_2Q

通过研究分圆多项式Φn(a,b)在n的两个素因子处的离散赋值,首先给出Gn(Q)是K2Q的子群时,Φn(a,b)所需满足的丢番图方程,然后证明了G55(Q)不是K2Q的子群,从而部分证明了B rowk in的一个猜想。

This paper, through investigating discrete valuation of cyclotomic polynomial Фn （ a, b） where n has two prime factors, presents the diophantine equation when Go （Q） is a subgroup of K2Q, then it proves that G55 （Q） is not a subgroup of K2Q, which confirms a special case of the conjecture proposed by Browkin.