Profinite Direct Sums with Applications to Profinite Groups of Type Φ_R

2025/04/07 by Tang, Jiacheng
Mathematics · #Rings, Modules, and Algebras #Finite Group Theory Research #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2504.05182

Abstract

We show that the "profinite direct sum" is a good notion of infinite direct sums for profinite modules having properties similar to direct sums of abstract modules. For example, the profinite direct sum of projective modules is projective, and there is a Mackey's Formula for profinite modules described using these sums. As an application, we prove that the class of profinite groups of type Φ_R is closed under subgroups.

Related

• Some aspects of profinite group theory
• Pontryagin duality and sheaves of profinite modules
• Modular Representations of Profinite Groups
• Algebraic properties of profinite groups
• Groups of profinite type and profinite rigidity