The quotients of the p-adic group ring of a cyclic group of order p

2025/04/12 by Maria Guedri, Guedri, Maria, Yassine Guerboussa +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2504.09239

Abstract

We classify, up to isomorphism, the ℤ_pG-modules of rank 1 (i.e., the quotients of ℤ_pG) for G cyclic of order p, where ℤ_p is the ring of p-adic integers. This allows us in particular to determine effectively the quotients of ℤ_pG which are cohomologically trivial over G. There are natural zeta functions associated to ℤ_pG for which we give an explicit formula.

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