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The Sylow Subgroups of a Finite Reductive Group
by Michel Enguehard   Jean Michel

Vol. 13 No. 2 (2018) P.227~P.247
 DOI: https://doi.org/10.21915/BIMAS.2018203 10.21915/BIMAS.2018203

ABSTRACT

We describe the structure of Sylow $\ell$-subgroups of a finite reductive group $\mathbf G(\mathbb F_q)$ when $q\not\equiv 0 \pmod \ell$ that we find governed by a complex reflection group attached to $\mathbf G$ and $\ell$, which depends on $\ell$ only through the set of cyclotomic factors of the generic order of $\mathbf G(\mathbb F_q)$ whose value at $q$ is divisible by $\ell$. We also tackle the more general case of groups $\mathbf G^F$ where $F$ is an isogeny some power of which is a Frobenius morphism.

KEYWORDS
reductive groups, Sylow subgroups.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20G40, 20D20.

MILESTONES