关于有理数域Q上多项式f(x)与f(x^m)的Galois群的阶

ON ORDER OF GALOIS’ GROUP OF POLYNOMIALS f(x) AND f(x^m) IN THE RATIONAL FIELD

确定有理数域Q上多项式f(x)的Galois群的阶是一件非常有意义的事情 .本文把文献 [1 ]中当m为奇数 ,多项式f(x)的Galois群的阶确定f(xm)的Galois群的阶的方法 ,推广到了m为偶时 ,对f(xm)的条件作进一步限制后 ,得到相同的结论 .同时给出了m =2时 ,对f(x2 )

It is a very sense thing to determine the order of Galois’ group of polynomial. The paper is to extent m as even for restriction condition of f(x^m) and reaches the same conclusion which \ determines the method of the order of Galois’ group of polynomial f(x) and f(x^m) in rational field. At the same time, we give the conclusion of m=2 by weakening the condition f(x^2).