TY - JOUR

T1 - Radical subgroups of the finite exceptional groups of Lie type E6

AU - An, Jianbei

AU - Dietrich, Heiko

AU - Huang, Shih Chang

N1 - Funding Information:
The authors thank Ji-ping Zhang for a discussion of Proposition 3.1 a); they thank Ronald Solomon and the referees for helpful comments and improvements, and observing that Theorem A could be extended to primes . The first author was supported by the Marsden Fund (of New Zealand), via award number UOA 1015 . The second author was supported by an ARC-DECRA Fellowship , project DE140100088 ; he thanks the National Science Council Taiwan (project NSC 102-2115-M-006-004 ) and the National Center for Theoretical Sciences (South) (project NSC 103-2119-M-006-001 ), Taiwan, for the financial support and great hospitality during a research visit to the National Cheng Kung University. The third author was supported by the National Science Council Taiwan (project NSC 102-2115-M-006-004 ) and the National Center for Theoretical Sciences (South) (project NSC 103-2119-M-006-001 ), Taiwan.

PY - 2014/7/1

Y1 - 2014/7/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jalgebra.2014.03.030

DO - 10.1016/j.jalgebra.2014.03.030

M3 - Article

AN - SCOPUS:84899140101

SN - 0021-8693

VL - 409

SP - 387

EP - 429

JO - Journal of Algebra

JF - Journal of Algebra

ER -