域Q(a^(1/s))上方程f(x)=0的Galois群

The Galois Group of f(x)=0 Based on Q(a^(1/s))

重点讨论Q(a～(1/s))域上的方程f(x)=0的Galois群的计算.给出并且证明了命题:域Q(a～(1/s))上f(x)=0的Galois群是f(x)=0在Q上的Galois群的子群,特别如果f(x)不含xS-a的因子,即f(x)的系数中没有sa的某个组合,则f(x)在Q(a～(1/s))的Galois群与f(x)在Q上的Galois群等同.并用具体实例来展示命题的实际意义.

The emphasis is laid on the root finding of function f(x)=0 over Q(a^(1/s)).The given proposition:Galois group of f(x)=0 over Q(a^(1/s)) is a sub-group of Galois group over Q.Particularly,if xs-a is not a factor of f(x),i.e.coefficients of f(x) are not in the form of combination of sa,then Galois groups of f(x) over Q and Q(a^(1/s)) are identical.Examples are given to show the practical meaning of the given proposition.