| Autor: |
TIMOTHY C. BURNESS, DONNA M. TESTERMAN |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
|
| Zdroj: |
Forum of Mathematics, Sigma, Vol 7 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
2050-5094 |
| DOI: |
10.1017/fms.2019.12 |
| Popis: |
Let $G$ be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic $p>0$ and let $X=\text{PSL}_{2}(p)$ 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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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