Relatively projective pro-p groups

2022/08/27 by Dan Haran, Haran, Dan, Pavel Zalesskii +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2208.12982

openalex publication_date 2022/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that the Kurosh Subgroup Theorem does not hold for pro-p groups of big cardinality. However, a subgroup G of a free pro-p product is projective relative to the Kurosh family of subgroups. In this paper we prove the converse of this fact.

Related

• Kurosh Subgroup Theorem in Free Pro-p Products
• Relatively projective profinie groups
• Pro-p groups with constant generating number on open subgroups
• Splitting theorems for pro-p groups acting on pro-p trees and 2-generated subgroups of free pro-p products with procyclic amalgamations
• Higher dimensional algebraic fiberings for pro-p groups