On the Hilbert 5-Class Field Towers of Some Pure Metacyclic Fields and Total Capitulation

Authors

  • Fouad Elmouhib
  • Abdelmalek Azizi
  • Mohamed Talbi

Keywords:

Groups of maximal class, 5-class field, Transfer, 5-class groups.

Abstract

In this paper, we study the length of the Hilbert 5-class field towers of some pure metacyclic fields of degree 20 over Q, which are the normal closure of some pure quintic fields, by means of some results of 5-groups. The capitulation problem is investigated too.

Keywords: Groups of maximal class, 5-class field, Transfer, 5-class groups.

2020 Mathematics Subject Classification. 20D15; 20D35; 11R29; 11R37

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Published

2025-04-09

How to Cite

Fouad Elmouhib, Abdelmalek Azizi, & Mohamed Talbi. (2025). On the Hilbert 5-Class Field Towers of Some Pure Metacyclic Fields and Total Capitulation. Jordan Journal of Mathematics and Statistics, 18(1), 17–25. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/661

Issue

Vol. 18 No. 1 (2025)

Section

Articles