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A new maximal subgroup of E8 in characteristic 3

Lookup NU author(s): Dr David StewartORCiD

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Abstract

© 2022 American Mathematical Society. We prove the existence and uniqueness up to conjugacy of a new maximal subgroup of the algebraic group of type E8 in characteristic 3. This has type F4, 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 = 3D4(2), namely that if H embeds in E8 (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 F4 subgroup.

Publication metadata

Author(s): Craven DA, Stewart DI, Thomas AR

Publication type: Article

Publication status: Published

Journal: Proceedings of the American Mathematical Society

Year: 2022

Volume: 150

Issue: 4

Pages: 1435-1448

Print publication date: 01/04/2022

Online publication date: 20/01/2022

Acceptance date: 04/07/2021

Date deposited: 10/11/2021

ISSN (print): 0002-9939

ISSN (electronic): 1088-6826

Publisher: American Mathematical Society

URL: https://doi.org/10.1090/proc/15759

DOI: 10.1090/proc/15759

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