Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584827 | Journal of Algebra | 2014 | 43 Pages |
Abstract
We consider the finite exceptional groups of Lie type E6+1(q)=E6(q) and E6â1(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 pâ¤q and qâ¡Îµmodp, and for p=3 with 3â¤q and qâ¡âεmod3. 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jianbei An, Heiko Dietrich, Shih-Chang Huang,