A1 -type subgroups containing regular unipotent elements

Tim Burness, Donna Testerman

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Abstract

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.
Original languageEnglish
Article numbere12
Number of pages61
JournalForum of Mathematics, Sigma
Volume7
Early online date24 Apr 2019
DOIs
Publication statusPublished - 2019

Keywords

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

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