-TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS
Keyword(s):
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.
1996 ◽
pp. 1-120
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2012 ◽
Vol 11
(02)
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pp. 1250038
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2008 ◽
Vol 4
(1)
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pp. 91-100
2016 ◽
Vol 19
(1)
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pp. 235-258
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1971 ◽
Vol 12
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pp. 1-14
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1976 ◽
Vol 79
(3)
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pp. 401-425
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2008 ◽
Vol 11
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pp. 280-297
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1992 ◽
Vol 111
(2)
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pp. 267-272
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2018 ◽
Vol 2020
(2)
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pp. 344-366
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