Cohomology of uniserial p-adic space groups with cyclic point group

2017/06/21 by Oihana Garaialde Ocaña, Ocaña, Oihana Garaialde
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR

paper · pdf · doi:10.48550/arxiv.1706.06753

arxiv created 2017/06/21 · openalex publication_date 2017/06/21 · arxiv updated 2017/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a fixed prime number and let R denote a uniserial p-adic space group of dimension d_x=(p-1)p^x-1 and with cyclic point group of order p^x. In this short note we prove that all the quotients of R of size bigger than or equal to p^d_x+x have isomorphic mod p cohomology groups. In particular, we show that the cohomology groups of sufficiently large quotients of the unique maximal class pro-p group are isomorphic as \F_p-modules.

Related

• The quotients of the p-adic group ring of a cyclic group of order p
• Cohomological uniqueness of some p-groups
• Rank, coclass and cohomology
• Cohomology of p-groups of nil potency class smaller than p
• p-adic geometry