Radical subgroups of the finite exceptional groups of Lie type E6

Jianbei An, Heiko Dietrich, Shih Chang Huang

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider the finite exceptional groups of Lie type E6+1(q)=E6(q) and E6-1(q)=E62(q), both the universal versions. We classify, up to conjugacy, the maximal p-local subgroups and radical p-subgroups of G=E6ε(q) for p ≥ 5 with p = q and q ε mod p, and for p = 3 with 3 q and q - ε mod 3. As an application, the essential p-rank of the Frobenius category FD(G) is determined, where D is a Sylow p-subgroup of G. Moreover, if p = 3, then we show that there is a subgroup H = F4(q) of G containing D such that FD(G)=FD(H), that is, H controls 3-fusion in G.

Original languageEnglish
Pages (from-to)387-429
Number of pages43
JournalJournal of Algebra
Volume409
DOIs
Publication statusPublished - 2014 Jul 1

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Groups of Lie Type
Subgroup
P-rank
Conjugacy
Frobenius
Fusion
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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

An, Jianbei ; Dietrich, Heiko ; Huang, Shih Chang. / Radical subgroups of the finite exceptional groups of Lie type E6. In: Journal of Algebra. 2014 ; Vol. 409. pp. 387-429.
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Radical subgroups of the finite exceptional groups of Lie type E6. / An, Jianbei; Dietrich, Heiko; Huang, Shih Chang.

In: Journal of Algebra, Vol. 409, 01.07.2014, p. 387-429.

Research output: Contribution to journalArticle

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