Finite groups containing an intrinsic 2-component of Chevalley type over a field of odd order

Harris, Morton E.

doi:10.1090/S0002-9947-1982-0656480-3

Finite groups containing an intrinsic $2$-component of Chevalley type over a field of odd order
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Trans. Amer. Math. Soc. 272 (1982), 1-65 Request permission

Abstract:

This paper extends the celebrated theorem of Aschbacher that classifies all finite simple groups $G$ containing a subgroup $L \cong {\text {SL}}(2,q)$, $q$ odd, such that $L$ is subnormal in the centralizer in $G$ of its unique involution. Under the same embedding assumptions, the main result of this work allows $L$ to be almost any Chevalley group over a field of odd order and determines the resulting simple groups $G$. The results of this paper are an essential ingredient in the current classification of all finite simple groups. Major sections are devoted to deriving various properties of Chevalley groups that are required in the proofs of the three theorems of this paper. These sections are of some independent interest.

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Notes on the

-conjecture

Characterization of Chevalley groups

Finite groups

Characterization of Chevalley groups