Automorphism groups of right-angled buildings: simplicity and local splittings
Automorphism groups of right-angled buildings: simplicity and local splittings
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直角建筑物的自同构群：简单性和局部分裂
DOI：
10.4064/fm224-1-2
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发表时间：
2012
影响因子：
0.6
通讯作者：
P. Caprace
中科院分区：
文献类型：
--
作者：
P. Caprace
证明了任意不可约半正则厚直角建筑的保型自同构群是抽象简单的。当建筑物是局部有限的，这就给出了一大族紧生成的抽象简单局部紧群。在适当的情况下，我们得到了这样的简单群的例子，这些简单群是局部不可分解的，但有局部正规子群分解为直接积，其所有因子都是局部正规的。
We show that the group of type-preserving automorphisms of any irreducible semiregular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated abstractly simple locally compact groups. Specialising to appropriate cases, we obtain examples of such simple groups that are locally indecomposable, but have locally normal subgroups decomposing non-trivially as direct products, all of whose factors are locally normal.