Abstract
Let G be a semisimple simply connected algebraic group defined and split over the field Fp with p elements, G(Fq) be the finite Chevalley group consisting of the Fq-rational points of G where q=pr, and Gr be the rth Frobenius kernel of G. This paper investigates relationships between the extension theories of G, G(Fq), and Gr over the algebraic closure of Fp. First, some qualitative results relating extensions over G(Fq) and Gr are presented. Then certain extensions over G(Fq) and Gr are explicitly identified in terms of extensions over G.
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