Determining class groups as Galois modules up to equivalence for some nonabelian extensions

2025/08/21 by Cornélius Greither, Greither, Cornelius, Takenori Kataoka +1
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2508.15242

openalex publication_date 2025/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In previous papers, the Galois module structure of minus class groups was studied for abelian CM extensions. In this paper, we discuss some nonabelian cases, focusing on metacyclic extensions. For a certain class of these, we obtain a complete description of the Galois modules that occur as minus class groups, modulo a certain equivalence relation on modules, which was introduced earlier by the same authors.

Citations

• On the Galois module structure of minus class groups

Related

• On the Galois module structure of minus class groups
• Galois action on class groups
• Galois p-groups and Galois modules
• Galois Module Structure of pth-Power Classes of Extensions of Degree p
• Galois module structure of the units modulo p^m of cyclic extensions of degree pⁿ