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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Vydané v:	Journal of number theory Ročník 180; s. 251 - 279
Hlavní autori:	Huang, Hau-Wen, Li, Wen-Ching Winnie
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 01.11.2017
Predmet:	Divide-and-conquer algorithms Galois closures Iterative algorithms 68W05 Iterative algorithms Divide-and-conquer algorithms 11R32 Galois closures
ISSN:	0022-314X, 1096-1658
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Popis
Shrnutí:	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