Construction of 2-local finite groups of a type studied by Solomon and Benson: Correction

TL;DR

This paper corrects an earlier error regarding the conjugacy classes of elementary abelian subgroups in Benson-Solomon fusion systems, confirming that the main results remain valid after correction.

Contribution

It provides a correction to previous work on Benson-Solomon fusion systems, clarifying the conjugacy class structure without altering the main conclusions.

Findings

Two conjugacy classes of elementary abelian subgroups of rank 3 exist in each fusion system

The correction does not affect the main results of the original paper

Clarifies subgroup classification in Benson-Solomon fusion systems

Abstract

We correct an error in Lemma 3.1 of my paper coauthored with Ran Levi on the Benson-Solomon fusion systems, and show that the change does not affect any of the other results in that paper. More precisely, as pointed out to us by Justin Lynd, there are two conjugacy classes of elementary abelian subgroups of rank $3$ in each of the fusion systems $\cal{F}_{{\rm Sol}}(q)$, and not only one as claimed in our paper.