The Reductive Subgroups of G_2

Abstract

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 $\sigma$ denote a standard Frobenius automorphism of $G$ such that $G_{\sigma }\cong G_2(q)$ with $q\ge 4$. In this paper we find all reductive subgroups of $G$ and quasi-simple subgroups of $G_{\sigma }$ in the defining characteristic.

18 pages; copy submitted to Journal of Group Theory