On the capitulation problem of some pure metacyclic fields of degree 20 II

2021/09/09 by Elmouhib, Fouad, Talbi, Mohemed, Azizi, Abdelmalek
#11R04 #11R18 #11R29 #11R37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2109.05943

Abstract

Let n be a 5^th power-free naturel number and k₀ = ℚ(ζ₅) be the cyclotomic field generated by a primitive 5^th root of unity ζ₅. Then k = ℚ(√[5]n,ζ₅) is a pure metacyclic field of absolute degree 20. In the case that k possesses a 5-class group C_k,5 of type (5,5) and all the classes are ambiguous under the action of Gal(k/k₀), the capitulation of 5-ideal classes of k in its unramified cyclic quintic extensions is determined.

Related

• On the capitulation problem of some pure metacyclic fields of degree 20
• On the exact divisibility by 5 of the class number of some pure metacyclic fields
• The generators of 5-class group of some fields of degree 20 over ℚ
• Capitulation in the absolutely abelian extensions of some number fields II
• 5-Class towers of cyclic quartic fields arising from quintic reflection