In the classification of finite simple groups, there is a major division between group of characteristic 2 type, where involutions resemble unipotent elements, and other groups, where involutions resemble semisimple elements.
Groups of characteristic 2 type and rank at least 3 are classified by the trichotomy theorem.
denotes the 2-core, the largest normal 2-subgroup of M, which is the intersection of all conjugates of any given Sylow 2-subgroup.
If this condition holds for all maximal 2-local subgroups M then G is said to be of characteristic 2 type.
Gorenstein, Lyons & Solomon (1994, p.55) use a modified version of this called even type.