David A. Craven, David I. Stewart, Adam R. Thomas
Published 2021-03-22Version 1
We prove the existence and uniqueness of a new maximal subgroup of the algebraic group of type $E_8$ in characteristic $3$. This has type $F_4$, and was missing from previous lists of maximal subgroups produced by Seitz and Liebeck--Seitz. We also prove a result about the finite group $H={}^3\!D_4(2)$, that if $H$ embeds in $E_8$ (in any characteristic $p$) and has two composition factors on the adjoint module then $p=3$ and $H$ lies in this new maximal $F_4$ subgroup.
The number of composition factors of order $p$ in completely reducible groups of characteristic $p$
The dimension of solution sets to systems of equations in algebraic groups
Splitting of Sharply 2-Transitive Groups of Characteristic 3
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