Uniqueness case

In mathematical finite group theory, the uniqueness case is one of the three possibilities for groups of characteristic 2 type given by the trichotomy theorem.
The uniqueness case covers groups "G" of characteristic 2 type with "e"("G") ≥ 3 that have an almost strongly "p"-embedded maximal 2-local subgroup for all primes "p" whose 2-local "p"-rank is sufficiently large (usually at least 3).
 proved that there are no finite simple groups in the uniqueness case.