### 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 language | English |
---|---|

Pages (from-to) | 387-429 |

Number of pages | 43 |

Journal | Journal of Algebra |

Volume | 409 |

DOIs | |

Publication status | Published - 2014 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

_{E6}.

*Journal of Algebra*,

*409*, 387-429. https://doi.org/10.1016/j.jalgebra.2014.03.030

}

_{E6}',

*Journal of Algebra*, vol. 409, pp. 387-429. https://doi.org/10.1016/j.jalgebra.2014.03.030

**Radical subgroups of the finite exceptional groups of Lie type _{E6}.** / An, Jianbei; Dietrich, Heiko; Huang, Shih Chang.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - An, Jianbei

AU - Dietrich, Heiko

AU - Huang, Shih Chang

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.

UR - http://www.scopus.com/inward/record.url?scp=84899140101&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899140101&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2014.03.030

DO - 10.1016/j.jalgebra.2014.03.030

M3 - Article

AN - SCOPUS:84899140101

VL - 409

SP - 387

EP - 429

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

_{E6}. Journal of Algebra. 2014 Jul 1;409:387-429. https://doi.org/10.1016/j.jalgebra.2014.03.030