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Let $q$ be a nontrivial odd prime power, and let $n \ge 2$ be a naturalnumber with $(n,q) \ne (2,3)$. We characterize the groups $PSL_n(q)$ and$PSU_n(q)$ by their $2$-fusion systems. This contributes to a programme ofAschbacher aiming at a simplified proof of the classification of finite simplegroups.

A characterization of the groups $PSL_n(q)$ and $PSU_n(q)$ by their $2$-fusion systems, $q$ odd