Results in the previous parts have reduced the choices for L, V in the Fun-
damental Setup (3.2.1) to the case where L/0 2 ,z(L) is essentially a group of Lie
type defined over F 2 , and Vis highly restricted. We adopt the convention that A5
(regarded as D,4(2)), and A1 (a subgroup of As~ £4(2) ~ nt(2)) are considered
to be defined over F 2. For a precise description of the pairs L, V which remain to
be considered, see conclusion (3) of Theorem 12.2.2 early in this part.
The first chapter 12 of this part contains a number of useful reductions which
smooth out the situation. For example, some reductions treat or eliminate certain
larger possibilities for Lor V. These reductions use special and comparatively ele-
mentary techniques, such as the weak-closure methods from section E.3, or control
of centralizers of certain elements of V.
The cases that remain after these sections are then treated in chapters 13 and
14, using "generic" techniques for groups over F 2 , such as versions of the theory of
large extraspecial 2-subgroups in the original classification literature, and variants
on the amalgam method from section F.9