Let G be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic p > 0 and let X = PSL2(p) be a subgroup of G containing a regular unipotent element x of G . By a theorem of Testerman, x is contained in a connected subgroup of G of type A1 . In this paper we prove that with two exceptions, X itself is contained in such a subgroup (the exceptions arise when (G, p) = (E6, 13) or (E7, 19) ). This extends earlier work of Seitz and Testerman, who established the containment under some additional conditions on p and the embedding of X in G . We discuss applications of our main result to the study of the subgroup structure of finite groups of Lie type.
- 2010 Mathematics Subject Classification:
- 20E07 (secondary)
- 20G41 (primary)