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.