Polynomials with Frobenius groups of prime degree as Galois groups II
Polynomials with Frobenius groups of prime degree as Galois groups II
复制标题
具有素次弗罗贝尼乌斯群的多项式为伽罗瓦群 II
DOI：
10.1016/0022-314x(86)90038-7
复制
发表时间：
1986
影响因子：
0.7
通讯作者：
N. Yui
中科院分区：
文献类型：
--
作者：
A. Bruen;C. U. Jensen;N. Yui
给出了q上p次≥5素数多项式的特征定理，其中p次Frobenius群：Fpl=FLp‘，L|p−1为Galois群.利用第p类切比雪夫多项式构造了一个具有伽罗瓦群Fp(p−1)2(p≡3(Mod 4))的一般多项式族.此外，还给出了一个具有Galois群F20的五次多项式的参数族。给出了F2p=Dp(p≤19)，F2 0，以及p=7和11的Fp(p−1)2的多项式的具体例子，并讨论了Frobenius域的一些性质.
We present characterization theorems for polynomials of prime degree p≥ 5 over Q with Frobenius groups of degree p: F pl= F lp′, l| p− 1 as Galois groups. We construct a generic family of polynomials with Galois group F p (p− 1) 2 (p≡ 3 (mod 4)), using the pth Chebyshev polynomial of the first kind. In addition, a parametric family of quintic polynomials with Galois group F 20 is given. Explicit examples of polynomials are presented for F 2p= D p (p≤ 19), F 20 and for F p (p− 1) 2 with p= 7 and 11. Some properties of Frobenius fields are also discussed.