Some groups of type VF
Some groups of type VF
复制标题
一些VF型群体
DOI：
10.1007/s00222-002-0254-7
复制
发表时间：
2003
影响因子：
3.1
通讯作者：
Brita Nucinkis
中科院分区：
文献类型：
--
作者：
I. Leary;Brita Nucinkis
一个群是VF型群，如果它有一个有限指标子群，而子群有一个有限分类空间。我们构造了其中某些有限阶元的中心化子不为VF型的VF型群和含有无穷多个有限子群共轭类的VF型群。因此，VF型群G不需要允许有限型泛真G-空间。我们构造了群G，使得泛真G-空间的最小维数严格大于G的虚上同调维数。我们的每一个组都嵌入GLm（λ）中，以获得足够大的值。还考虑了K-理论的一些应用。
A group is of typeVFif it has a finite-index subgroup which has a finite classifying space. We construct groups of typeVFin which the centralizers of some elements of finite order are not of typeVFand groups of typeVFcontaining infinitely many conjugacy classes of finite subgroups. It follows that a groupGof typeVFneed not admit a finite-type universal properG-space. We construct groupsGfor which the minimal dimension of a universal properG-space is strictly greater than the virtual cohomological dimension ofG. Each of our groups embeds inGLm(ℤ) for sufficiently largem. Some applications toK-theory are also considered.