A unified approach to the Galois closure problem

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 locall...

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Bibliographic Details
Published in:Journal of number theory Vol. 180; pp. 251 - 279
Main Authors: Huang, Hau-Wen, Li, Wen-Ching Winnie
Format: Journal Article
Language:English
Published: Elsevier Inc 01.11.2017
Subjects:
Divide-and-conquer algorithms
Galois closures
Iterative algorithms
68W05
Iterative algorithms
Divide-and-conquer algorithms
11R32
Galois closures
ISSN:0022-314X, 1096-1658
Online Access:Get full text
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Summary: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 étale 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.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2017.04.011