A new maximal subgroup of E8 in characteristic 3

David Craven, David Stewart, Adam Thomas

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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.
Original languageEnglish
Pages (from-to)1435–1448
JournalProceedings of the American Mathematical Society
Issue number4
Early online date20 Jan 2022
Publication statusPublished - Apr 2022


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