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A new maximal subgroup of ₈ in characteristic 3
Journal article   Open access   Peer reviewed

A new maximal subgroup of ₈ in characteristic 3

David Craven, David Stewart and Adam Thomas
Proceedings of the American Mathematical Society, Vol.150(4), pp.1435-1448
04/2022
DOI: 10.1090/proc/15759
url
https://research.manchester.ac.uk/en/publications/db230b16-b6b9-474a-9e26-634b8f986634View
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Abstract

We prove the existence and uniqueness up to conjugacy of a new maximal subgroup of the algebraic group of type E 8 E_8 in characteristic 3 3 . This has type F 4 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 ) H={}^3\!D_4(2) , namely that if H H embeds in E 8 E_8 (in any characteristic p p ) and has two composition factors on the adjoint module then p = 3 p=3 and H H lies in a conjugate of this new maximal F 4 F_4 subgroup.

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