A unified approach to the Galois closure problem

作者：Huang Hau Wen^*; Li Wen Ching Winnie

来源：Journal of Number Theory, 2017, 180: 251-279.

DOI：10.1016/j.jnt.2017.04.011

• o Galois closures
• Iterative algorithms
• Divide-and-conquer algorithms

In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a connected undirected graph, finite covering spaces of a locally connected topological space, finite etale covers of a smooth projective irreducible algebraic variety, and finite covers of normal varieties. We present two algorithms whose outputs are shown to be desired Galois closures. An upper bound of the degree of the Galois closure under each algorithm is also obtained.

• 出版日期2017-11
• 单位中央民族大学