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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A new maximal subgroup of $E_8$ in characteristic $3$
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by David A. Craven, David I. Stewart and Adam R. Thomas PDF
Proc. Amer. Math. Soc. 150 (2022), 1435-1448 Request permission

Abstract:

We prove the existence and uniqueness up to conjugacy 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 $H={}^3\!D_4(2)$, namely 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 a conjugate of this new maximal $F_4$ subgroup.
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Additional Information
  • David A. Craven
  • Affiliation: School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
  • MR Author ID: 833948
  • Email: d.a.craven@bham.ac.uk
  • David I. Stewart
  • Affiliation: School of Mathematics, Statistics and Physics, Herschel Building, Newcastle University, Newcastle NE1 7RU, United Kingdom
  • MR Author ID: 884527
  • Email: david.stewart@ncl.ac.uk
  • Adam R. Thomas
  • Affiliation: Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom
  • MR Author ID: 1091953
  • Email: Adam.R.Thomas@warwick.ac.uk
  • Received by editor(s): April 22, 2021
  • Received by editor(s) in revised form: June 28, 2021
  • Published electronically: January 20, 2022
  • Additional Notes: The first author was supported by the Royal Society during the course of this research
  • Communicated by: Martin Liebeck
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 1435-1448
  • MSC (2020): Primary 20G41
  • DOI: https://doi.org/10.1090/proc/15759
  • MathSciNet review: 4375734