Introduction to Volume II
The treatment of the "quasithin groups of even characteristic" is one of the
major steps in the Classification of the Finite Simple Groups (for short, the Clas-
sification). Geoff Mason announced a classification of a subclass of the quasithingroups in about 1980, but he never published his work, and the preprint he dis-
tributed [Mas] is incomplete in various ways. In two lengthy volumes, we treat the
quasithin groups of even characteristic; in particular we close that gap in the proof
of the Classification.Each volume contains an Introduction discussing its contents. For further back-
ground, the reader may also wish to consult the Introduction to Volume I; that
volume records and develops the machinery needed to prove our Main Theorem,which classifies the simple quasithin JC-groups of even characteristic. Volume II
implements the proof of the Main Theorem.Section 0.1 of this Introduction to Volume II gives the statement of the two
main results of the paper, together with a few definitions necessary to state those
results. Section 0.2 discusses the role of quasithin groups in the larger context of
the Classification; we also compare the hypotheses of the original quasithin problemwith those of more recent alternatives, and give some history of the problem. In
sections 0.3 and 0.4, we introduce further fundamental concepts and notation, andgive an outline of the proofs of our two main theorems.
The Introduction to Volume I describes the references we appeal to during the
course of the proof; see section 0.12 on recognition theorems and section 0.13 on
Background References.0.1. Statement of Main Results
We begin by defining the class of groups considered in our Main Theorem, and
since the definitions are somewhat technical, we also supply some motivation. For
definitions of more basic group-theoretic notation and terminology, the reader is
directed to Aschbacher's text [Asc86a].
The quasithin groups are the "small" groups in that part of the Classification
where the actual examples are primarily the groups of Lie type defined over a field
of characteristic 2. We first translate the notion of the "characteristic" of a linear
group into the setting of abstract groups: Let G be a finite group, T E Syb(G),
and let M denote the set of maximal 2-local subgroups of G.^1 We define G to be
of even characteristic if
(^1) A 2-local subgroup is the.normalizer of a nonidentity 2-subgroup.
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