标题： 第二3类群的余类 显示英文标题

标题： Coclass of the second 3-class group

摘要： 通过有限幂零3-群的参数化表示，证明了任何代数数域K的第二3-类群M=Gal(F_3^2(K)/K)的上同调类cc(M)，当K的初等双循环3-类群Cl_3(K)=(3,3)时，由四个无限制循环三次扩张E_i (i=1,..,4)的3-类群中第二个最大阶ord(Cl_3(E_2))=3^{cc(M) + 1}唯一确定。作为应用，从3-类数ord(Cl_3(E_i))的广泛数据库中计算了具有指定上同调类cc(M)的二次和三次域K的最小判别式。 显示英文摘要

摘要： By means of parametrized presentations of finite metabelian 3-groups, it is proved that the coclass cc(M) of the second 3-class group M=Gal(F_3^2(K)/K) of any algebraic number field K with elementary bicyclic 3-class group Cl_3(K)=(3,3) is determined unambiguously by the second largest order ord(Cl_3(E_2))=3^{cc(M)+1} among the four 3-class groups of the unramified cyclic cubic extensions E_i (i=1,..,4) of K. Minimal discriminants of quadratic and cubic fields K with assigned coclass cc(M) are computed from extensive databases of 3-class numbers ord(Cl_3(E_i)) as an application.