Control of fixed points over discrete $p$-toral groups, and existence and uniqueness of linking systems

TL;DR

This paper extends results on the existence and uniqueness of linking systems for saturated fusion systems over discrete p-toral groups, removing the reliance on the classification of finite simple groups.

Contribution

It generalizes previous results by removing the need for the classification of finite simple groups in establishing linking systems for discrete p-toral groups.

Findings

Extended results on linking systems to broader classes of groups.

Removed the dependence on the classification of finite simple groups.

Provided new methods for analyzing fixed points over discrete p-toral groups.

Abstract

The existence and uniqueness of linking systems associated to saturated fusion systems over discrete $p$-toral groups were proved by Levi and Libman. Their proof make indirectly use of the classification of the finite simple groups. Here we extend some results and arguments of Glauberman and Lynd to show how to remove this assumption.