有限约化群的Sylow子群

IF 0.1 Q4 MATHEMATICS

Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2016-02-03 DOI:10.21915/BIMAS.2018203

Michel Enguehard, J. Michel

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引用次数: 12

摘要

我们描述了有限约化群G(Fq)的Sylow {\ell}-子群的结构，当q $\ \不\等分$ 0 (mod {\ell})时，我们发现它由附在G和{\ell}上的复反射群所控制，该群仅依赖于{\ell}，其值在q处可被{\ell}整除的G(Fq)的一般阶环切因子集。我们也处理更一般的情况gf，其中F是同基因，其幂是Frobenius态射。

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The Sylow Subgroups of a Finite Reductive Group

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

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来源期刊

Bulletin of the Institute of Mathematics Academia Sinica New Series MATHEMATICS-

自引率

50.00%

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