Galois群的一个表示

A Description of Galois Group

F是任意特征p的域,f(x)为F的不可约多项式,K为f(x)在F上的分裂域。在情况K/F为Galois扩域,K可看成F上的线性空间。在文中我们考虑σ∈G(K/F),σ在某基下的矩阵,特别的当σ为正规扩张时,可以找到一组基,使得σ在这组基下的矩阵是不变的。

F is an arbitrary field with characteristic p,f（x） is a irreducible polynomial over F. Let K be the splitting field off（x） over F. On the condition of K/F be Galois extension field,K can look as a vector space over F, in thin paper we consider arbitary σ ∈ G（K/F） , the matrix of σ under the some basis. Especially, when K/F is a normal extension field,we can find a basis such that the matrix of σ under the basis is invariant.