Construction of a cyclic p-extension of number fields whose unit group has prescribed Galois module structure | Synapse
October 19, 2025Open Access
Construction of a cyclic p-extension of number fields whose unit group has prescribed Galois module structure
Key Points
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.
Abstract
For any finite cyclic p-group G, we will show that every Zₚ-torsion free finitely generated ZₚG-module appears as OK^ₙZₚ up to ZₚG-free direct summands for a certain G-extension K/k of number fields.