The Reductive Subgroups of G_2

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Let $G:=G_2(K)$ be a simple algebraic group of type $G_2$ defined over an algebraically closed field $K$ of characteristic $p>0$. Let $σ$ denote a standard Frobenius automorphism of $G$ such that $G_σ\cong G_2(q)$ with $q\geq 4$. In this paper we find all reductive subgroups of $G$ and quasi-simple subgroups of $G_σ$ in the defining characteristic.
18 pages; copy submitted to Journal of Group Theory

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