Lightly ramified number fields with Galois group $S.M_{12}.A$

David P. Roberts

doi:10.5802/jtnb.948

Lightly ramified number fields with Galois group

S . M_{12} . A

David P. Roberts ¹

¹ Division of Science and Mathematics University of Minnesota Morris Morris, MN 56267, USA

Journal de théorie des nombres de Bordeaux, Volume 28 (2016) no. 2, pp. 435-460.

Abstract
Résumé

We specialize various three-point covers to find number fields with Galois group $M_{12}$ , $M_{12} . 2$ , $2 . M_{12}$ , or $2 . M_{12} . 2$ and light ramification in various senses. One of our $2 . M_{12} . 2$ fields has the unusual property that it is ramified only at the single prime $11$ .

Par spécialisation de divers revêtements à trois points, on trouve des corps de nombres ayant groupe de Galois $M_{12}$ , $M_{12} . 2$ , $2 . M_{12}$ , ou $2 . M_{12} . 2$ et petite ramification selon divers aspects. Un de ces corps, de groupe de Galois $2 . M_{12} . 2$ , a la propriété remarquable de n’être ramifié qu’en $11$ .

Received: 2014-04-01
Revised: 2014-08-25
Accepted: 2014-09-04
Published online: 2017-01-02

MR: 3509719 | Zbl: 1411.11102

DOI: 10.5802/jtnb.948

Classification: 11R21, 11R29, 11R32, 11G32
Keywords: Number field, Discriminant, Ramification, Mathieu group

Author's affiliations:

David P. Roberts ¹

¹ Division of Science and Mathematics University of Minnesota Morris Morris, MN 56267, USA

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     journal = {Journal de th\'eorie des nombres de Bordeaux},
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David P. Roberts. Lightly ramified number fields with Galois group $S.M_{12}.A$. Journal de théorie des nombres de Bordeaux, Volume 28 (2016) no. 2, pp. 435-460. doi : 10.5802/jtnb.948. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.948/

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