A group is said to be of
even characteristic if :C_M(O_2(M)) \le O_2(M) for all maximal 2-local subgroups
M that contain a
Sylow 2-subgroup of
G, where O_2(M) 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. use a modified version of this called
even type. ==References==