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


Author: Morton E. Harris
Journal: Trans. Amer. Math. Soc. 272 (1982), 1-65
MSC: Primary 20D05
DOI: https://doi.org/10.1090/S0002-9947-1982-0656480-3
MathSciNet review: 656480
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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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DOI: https://doi.org/10.1090/S0002-9947-1982-0656480-3
Article copyright: © Copyright 1982 American Mathematical Society

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