The saturated fusion systems on a Sylow 2-subgroup of ${\Omega}^+_8 (2)$

TL;DR

This paper classifies saturated fusion systems on a specific Sylow 2-subgroup of the group Ω⁺₈(2), focusing on those with trivial 2-core, and provides examples related to known groups.

Contribution

It identifies and classifies saturated fusion systems on a Sylow 2-subgroup of Ω⁺₈(2) with trivial 2-core, including examples from related groups.

Findings

Examples include fusion systems of Ω⁺₈(2), Ω⁺₈(2):3, PΩ⁺₈(3), and PΩ⁺₈(3):3.

The classification focuses on systems with trivial O₂(𝔽).

Provides explicit instances of such fusion systems.

Abstract

We consider saturated fusion systems $\mathcal F$ on a Sylow $2$-subgroup of $\Omega^+_8(2)$ with $O_2(\mathcal F) = 1$. Examples for this are the $2$-fusion systems of $\Omega^+_8(2)$, $\Omega^+_8(2):3$, $P\Omega^+_8(3)$ and $P\Omega^+_8(3):3$