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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory