Skip to Main content Skip to Navigation
Theses

Autour d'une conjecture de B. Gross relative à l'existence de corps de nombres de groupe de Galois non résoluble et ramifiés en un unique premier p petit

Abstract : The current research examines the conjecture made by B. Gross on the existence of several number fields with a nonsolvable Galois group and which are ramified at exactly one prime p less than 11.
The study concerns the number fields of degree n ≤ 9. First of all, we focus on the instruments of the analysis, before presenting the methods that we used to solve the problem.
The work of J. Jones showed that quintic and sextic number fields ramified only at one small prime are always solvable.
Also, S. Brueggeman showed that septic number fields ramified only at one small prime are always solvable.
We eliminate octic and nonic number fields ramified only at 5 by using a method which depend on GRH or inconditionally by computer search. Our computer search also shows that only the ramification at p = 2 for the octic number fields and the ramification at p = 3 for the nonic number fields are possible. Note that all of these fields found have a solvable Galois group. We conclude that Gross's question has a negative answer for nonsolvable Galois group inside S_n, for n ≤ 9.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-00012068
Contributor : Sylla Lesseni <>
Submitted on : Friday, March 31, 2006 - 5:24:29 PM
Last modification on : Thursday, January 11, 2018 - 6:12:20 AM
Long-term archiving on: : Saturday, April 3, 2010 - 9:20:18 PM

Identifiers

  • HAL Id : tel-00012068, version 1

Collections

IMB | CNRS | INSMI

Citation

Sylla Lesseni. Autour d'une conjecture de B. Gross relative à l'existence de corps de nombres de groupe de Galois non résoluble et ramifiés en un unique premier p petit. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2005. Français. ⟨tel-00012068⟩

Share

Metrics

Record views

227

Files downloads

253