Maximal 2-local subgroups of E7(q)

Jianbei An, Heiko Dietrich

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Let G=E7(q) be the finite exceptional group of Lie type (universal version). We classify, up to conjugacy, all maximal-proper 2-local subgroups of G, that is, all 2-local M<G which are maximal with respect to inclusion among all proper subgroups of G which are 2-local. For this purpose, we first determine, up to conjugacy, all elementary-abelian 2-subgroups of G containing the center Z(G). These classifications are an important first step towards a classification of the 2-radical subgroups of G.
Original languageEnglish
Pages (from-to)503-536
Number of pages34
JournalJournal of Algebra
Volume445
DOIs
Publication statusPublished - 2016

Keywords

  • Exceptional type
  • Finite groups of Lie type
  • Maximal local subgroups

Cite this

An, Jianbei ; Dietrich, Heiko. / Maximal 2-local subgroups of E7(q). In: Journal of Algebra. 2016 ; Vol. 445. pp. 503-536.
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Maximal 2-local subgroups of E7(q). / An, Jianbei; Dietrich, Heiko.

In: Journal of Algebra, Vol. 445, 2016, p. 503-536.

Research output: Contribution to journalArticleResearchpeer-review

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AU - An, Jianbei

AU - Dietrich, Heiko

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N2 - Let G=E7(q) be the finite exceptional group of Lie type (universal version). We classify, up to conjugacy, all maximal-proper 2-local subgroups of G, that is, all 2-local M<G which are maximal with respect to inclusion among all proper subgroups of G which are 2-local. For this purpose, we first determine, up to conjugacy, all elementary-abelian 2-subgroups of G containing the center Z(G). These classifications are an important first step towards a classification of the 2-radical subgroups of G.

AB - Let G=E7(q) be the finite exceptional group of Lie type (universal version). We classify, up to conjugacy, all maximal-proper 2-local subgroups of G, that is, all 2-local M<G which are maximal with respect to inclusion among all proper subgroups of G which are 2-local. For this purpose, we first determine, up to conjugacy, all elementary-abelian 2-subgroups of G containing the center Z(G). These classifications are an important first step towards a classification of the 2-radical subgroups of G.

KW - Exceptional type

KW - Finite groups of Lie type

KW - Maximal local subgroups

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JF - Journal of Algebra

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