Quadratic subfields of quaternion and dihedral extensions | Synapse
April 22, 2026
Quadratic subfields of quaternion and dihedral extensions
Key Points
The aim is to classify Galois extensions of number fields featuring a Klein group within quaternion or dihedral extensions.
Classifying Galois extensions of number fields
Analyzing the embedding of Klein groups
Exploring quaternion and dihedral extensions of order 2^{n+1}
All Galois extensions are classified for natural n ≥ 4.
Specific structures of the Klein group within extensions are detailed.
Significant algebraic connections are established in the context of number fields.
Abstract
For any natural n 4, we classify all Galois extensions K/k of number fields with Klein group embedded in a quaternion/dihedral extension of order 2^n+1.