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This is a Experimental Study study.

October 19, 2025Open Access

Construction of a cyclic p-extension of number fields whose unit group has prescribed Galois module structure

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Every Zp-torsion free finitely generated Zp[G]-module can occur as part of the unit group structure.
A specific G-extension K/k of number fields facilitates the appearance of these modules.
The results imply new understandings of the Galois module structure in number fields.
Exploration focuses on the interplay between these unit groups and cyclic p-groups for better modular insights.

Implication

This research demonstrates constructions of cyclic p-extensions in number fields, showing unit group configurations for finite cyclic p-groups, suggesting new Galois module possibilities.

Abstract

For any finite cyclic p-group G, we will show that every Zₚ-torsion free finitely generated Zₚ[G]-module appears as OK^×⊗ZZₚ up to Zₚ[G]-free direct summands for a certain G-extension $K/k$ of number fields.

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Cite This Study

Manabu Ozaki (2025) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc6970b8 https://doi.org/10.48550/arxiv.2507.12949

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Implication

This research demonstrates constructions of cyclic p-extensions in number fields, showing unit group configurations for finite cyclic p-groups, suggesting new Galois module possibilities.

Construction of a cyclic p-extension of number fields whose unit group has prescribed Galois module structure

Key Points

Implication

Abstract

Discussion

Cite This Study

Construction of a cyclic p-extension of number fields whose unit group has prescribed Galois module structure

Key Points

Implication

Abstract

Discussion

Cite This Study

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