## Abstract

Let

*G*be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic*p*> 0 and let*X*= PSL_{2}(*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*A*_{1}. In this paper we prove that with two exceptions,*X*itself is contained in such a subgroup (the exceptions arise when (*G*,*p*) = (*E*_{6}, 13) or (*E*_{7}, 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.Original language | English |
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Article number | e12 |

Number of pages | 61 |

Journal | Forum of Mathematics, Sigma |

Volume | 7 |

Early online date | 24 Apr 2019 |

DOIs | |

Publication status | Published - 2019 |

## Keywords

- 2010 Mathematics Subject Classification:
- 20E07 (secondary)
- 20E32
- 20G41 (primary)

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