Prime ideals of the Burnside ring of a saturated fusion system

TL;DR

This paper extends Dress's classical results on prime ideals of the Burnside ring from finite groups to saturated fusion systems, providing a comprehensive classification of these ideals and their inclusion relations.

Contribution

It introduces a typology for prime ideals of the Burnside ring of saturated fusion systems, generalizing known group-theoretic results to fusion systems.

Findings

Classifies prime ideals of A(F) for saturated fusion systems

Establishes inclusion relations among these prime ideals

Provides a framework analogous to Dress's results for finite groups

Abstract

In a 1969 article, A. Dress described the prime ideals of the Burnside ring of a finite group G and the inclusion relations between them. One may ask whether similar results exist for the Burnside ring of a saturated fusion system F on a finite p-group S. The present paper answers positively, providing a typology for the prime ideals of A(F) and for those of A(F) (p) as a consequence.