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October 16, 2025Open Access

Unramified extensions of quadratic number fields with Galois group 2. Aₙ

Key Points

Infinitely many groups 2.An are realized as unramified extensions in quadratic number fields, enhancing number theory.
This research provides the first comprehensive realizations of infinite covering groups in this context.
The study builds on previous works that only addressed conditional results, thus marking a significant advancement.
Use of Galois group theory establishes deeper connections between number fields and their algebraic structures.

Abstract

We realize infinitely many covering groups 2. Aₙ (where Aₙ is the alternating group) as the Galois group of everywhere unramified Galois extensions over infinitely many quadratic number fields. After several predecessor works investigating special cases or proving conditional results in this direction, these are the first unramified realizations of infinitely many of these groups.

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Joachim König (Thu,) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd2cd — DOI: https://doi.org/10.48550/arxiv.2505.10100

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Authors

Joachim König

Korea National University of Education

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Unramified extensions of quadratic number fields with Galois group 2. Aₙ

Key Points

Abstract

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Cite this study

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Authors

Actions

References and Citations

Citation Network

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Discussion

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