Fusion Systems for Profinite Groups

TL;DR

This paper introduces pro-fusion systems on pro-p groups, extending fusion systems to infinite groups, and proves an Alperin's Fusion Theorem analogue for these systems.

Contribution

It generalizes the concept of fusion systems to pro-p groups and establishes a foundational theorem analogous to Alperin's for these new structures.

Findings

Pro-fusion systems are defined on pro-p groups.

An Alperin's Fusion Theorem for pro-fusion systems is proved.

The work extends fusion theory to infinite groups.

Abstract

We introduce the notion of a pro-fusion system on a pro-p group, which generalizes the notion of a fusion system on a finite p-group. We also prove a version of Alperin's Fusion Theorem for pro-fusion systems.