# Extensions of the Benson-Solomon fusion systems

## TL;DR

This paper investigates the Benson-Solomon fusion systems, the unique known simple saturated fusion systems at prime two not originating from finite groups, by analyzing their automorphisms and potential extensions.

## Contribution

It determines the automorphism groups and possible almost simple extensions of Benson-Solomon fusion systems and their centric linking systems, advancing understanding of these unique structures.

## Key findings

- Automorphism groups of Benson-Solomon systems are characterized.
- Possible almost simple extensions are classified.
- Insights into the structure of centric linking systems are provided.

## Abstract

The Benson-Solomon systems comprise the only known family of simple saturated fusion systems at the prime two that do not arise as the fusion system of any finite group. We determine the automorphism groups and the possible almost simple extensions of these systems and of their centric linking systems.