A unified approach to the Galois closure problem
Number Theory
2017-07-04 v2
Abstract
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.
Cite
@article{arxiv.1507.04433,
title = {A unified approach to the Galois closure problem},
author = {Hau-Wen Huang and Wen-Ching Winnie Li},
journal= {arXiv preprint arXiv:1507.04433},
year = {2017}
}