Relative property A and relative amenability for countable groups
Relative property A and relative amenability for countable groups
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DOI：
10.1016/j.aim.2012.07.030
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发表时间：
2011-09
影响因子：
1.7
通讯作者：
Ronghui Ji;C. Ogle;B. Ramsey
中科院分区：
文献类型：
--
作者：
Ronghui Ji;C. Ogle;B. Ramsey
我们定义了关于有限子群族的可数群的一个相对性质A。给出了相对性质A的许多刻画。特别地，相对有界上同调刻画表明，如果G相对于一族子群H有性质A，如果每个H∈H都有性质A，则G有性质A。特别地，如果群作用在局部有限性质A上，且有性质A的任何稳定子，则群是性质A。作为相对性质A的特例，引入了离散群相对从容的类似定义，得到了类似的结果。
We define a relative property A for a countable group with respect to a finite family of subgroups. Many characterizations for relative property A are given. In particular a relative bounded cohomological characterization shows that if G has property A relative to a family of subgroups H and if each H∈H has property A, then G has property A. This result leads to new classes of groups that have property A. In particular, groups are of property A if they act cocompactly on locally finite property A spaces of bounded geometry with any stabilizer of property A. Specializing the definition of relative property A, an analogue definition of relative amenability for discrete groups is introduced and similar results are obtained.