A New Maximal Subgroup of $E_8$ in Characteristic $3$

David A. Craven; David I. Stewart; Adam R. Thomas

A New Maximal Subgroup of $E_8$ in Characteristic $3$

Group Theory 2021-07-06 v2

Authors: David A. Craven , David I. Stewart , Adam R. Thomas

Abstract

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.

Keywords

maximal subgroup algebraic group e8 characteristic 3 f4 finite group composition factor

Cite

@article{arxiv.2103.12148,
  title  = {A New Maximal Subgroup of $E_8$ in Characteristic $3$},
  author = {David A. Craven and David I. Stewart and Adam R. Thomas},
  journal= {arXiv preprint arXiv:2103.12148},
  year   = {2021}
}

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12 pages. Proc. Amer. Math. Soc., to appear

A New Maximal Subgroup of $E_8$ in Characteristic $3$

Abstract

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