What question did this study set out to answer?

The aim is to classify Galois extensions of number fields featuring a Klein group within quaternion or dihedral extensions.

April 22, 2026Izvestiya Mathematics

Quadratic subfields of quaternion and dihedral extensions

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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.

Implication

Classification identifies Galois extensions of number fields with specific group structures, indicating important algebraic relationships.

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 2ⁿ⁺¹.

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Cite This Study

D. D. Kiselev (2026) studied this question.

synapsesocial.com/papers/69e8656e6e0dea528dde9fc5 https://doi.org/10.4213/im9636e

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Implication

Classification identifies Galois extensions of number fields with specific group structures, indicating important algebraic relationships.

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 2ⁿ⁺¹.

Quadratic subfields of quaternion and dihedral extensions

Key Points

Implication

Abstract

Discussion

Cite This Study

Quadratic subfields of quaternion and dihedral extensions

Key Points

Implication

Abstract

Discussion

Cite This Study

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