A new maximal subgroup of E8 in characteristic 3

David Craven; David Stewart; Adam Thomas

A new maximal subgroup of E₈ in characteristic 3

David Craven, David Stewart, Adam Thomas

Mathematics

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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 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 language	English
Pages (from-to)	1435–1448
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	4
Early online date	20 Jan 2022
Publication status	Published - Apr 2022

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First published in Proceedings of the American Mathematical Society in Volume 150, Number 4, April 2022, Pages 1435–1448, published by the American Mathematical Society. © 2022 American Mathematical Society
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title = "A new maximal subgroup of E8 in characteristic 3",

abstract = "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.",

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AB - 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.

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VL - 150

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EP - 1448

JO - Proceedings of the American Mathematical Society

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A new maximal subgroup of E8 in characteristic 3

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A new maximal subgroup of E₈ in characteristic 3