And the Phan-type Theorem of Type F 4
And the Phan-type Theorem of Type F 4
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以及F型4的Phan型定理
DOI：
10.1090/s0002-9947-2012-05694-7
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Stefan Witzel
中科院分区：
文献类型：
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作者：
Stefan Witzel
我们调整和完善[Abr 96]和[DGM]中开发的方法，以建立[BGHS 07]（Bn型）和[GHS 03]（Cn型）中定义的Phan几何形状的球形度及其推广。作为这个球性的应用，我们确定了群Sp 2n（Fq 2 [t，t]）的酉形式的拓扑有限长度（定理7.1），并给出了F4型的E-T型定理的首次公开证明（定理7.11）。除此之外，我们还得到了群Sp 2n（Fq 2 [t]）的拓扑有限长和Bn型和Cn型的n-型定理.在算术群理论中，我们关于Sp 2n（F q2 [t，t]）的酉形式的拓扑有限长度的结果是支持秩猜想的另一个例子，参见[Beh 98，p. 80]。在有限单群分类的修正中，F4型的E-T型定理的出版物总结了Phan定理[Pha 77 a]，[Pha 77 b]的修正及其对非简单花边图的扩展;参见。[AB08，第14.2节]（第656页）和[GLS 05]（第333页）。
We adapt and refine the methods developed in [Abr96] and [DGM] in order to establish the sphericity of the Phan geometries defined in [BGHS07] (type Bn) and [GHS03] (type Cn), and their generalizations. As applications of this sphericity we determine the topological finiteness length of the unitary form of the group Sp 2n (F q2 [t, t]) (Theorem 7.1) and give the first published proof of the Phan-type theorem of type F4 (Theorem 7.11). Apart from that we reproduce the topological finiteness length of the group Sp 2n (F q2 [t]) and the Phan-type theorems of types Bn and Cn. In the theory of arithmetic groups our result on the topological finiteness length of the unitary form of Sp 2n (F q2 [t, t]) is another example supporting the rank conjecture, see [Beh98, p. 80]. Within the revision of the classification of the finite simple groups this publication of the Phan-type theorem of type F4 concludes the revision of Phan’s theorems [Pha77a], [Pha77b] and their extension to the non-simply laced diagrams; cf. [AB08, Section 14.2] on page 656 and [GLS05] on page 333.