On the Galois Group of Unramified Extensions of a p-adic Field
DOI:
https://doi.org/10.17268/sel.mat.2026.01.06Keywords:
Frobenius automorphism, Galois group, unramified extensionAbstract
In this work, we study the structure of the Galois group of finite unramified extensions of the p-adic field. Furthermore, we establish the uniqueness, up to isomorphism, of unramified extensions of a given degree, and we describe the Galois group of the maximal unramified extension of Qp.
References
[1] Milne JS. Fields and Galois Theory. Version 4.21. 2008. Available from: http://www.jmilne.org/math/
[2] Stewart I, Tall D. Algebraic Number Theory and Fermat’s Last Theorem. 3rd ed. Natick (MA): A K Peters; 2002.
[3] Weintraub SH. Galois Theory. New York: Springer Science+Business Media; 2009.
[4] Mas R. Raíces p-ádicas de la unidad [tesis de maestría]. Lima: Pontificia Universidad Católica del Perú; 2015.
[5] Neukirch J. Algebraic Number Theory. Berlin: Springer; 1999.
[6] Robert A. A Course in p-adic Analysis. New York: Springer-Verlag; 2000.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Selecciones Matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
