Uniform non-amenability
Uniform non-amenability
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统一不服从
DOI：
10.1016/j.aim.2004.10.013
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
E. Ventura
中科院分区：
文献类型：
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作者：
G. Arzhantseva;J. Burillo;M. Lustig;Lawrence Reeves;H. Short;E. Ventura
对于任意有限生成群G，引入一个不变的F？lg⩾0来度量G的“不可修改量”.如果G是服从的，则F？lg=0.如果F？lg>；0，我们称G一致不可服从。我们研究了这个不变量的基本性质，例如，当它传递到G的子群和商时，它的行为。我们证明了以下几类群是一致不可服从的：非交换自由群，非初等字双曲群，大群，具有足够大的奇数指数的自由Burnside群，以及作用在树上的非单线性群。一致的不可随意性意味着一致的指数增长。我们还证明了一族非顺从群(特别是包括所有非可解的Baumgrag-Solitar群)不是一致非顺从的，也就是说，它们满足F？lg=0。最后，我们得到了关于G的左正则表示的一致Følner常数和一致Kazhdan常数之间的关系。
For any finitely generated group G an invariant FølG⩾0 is introduced which measures the “amount of non-amenability” of G. If G is amenable, then FølG=0. If FølG>0, we call G uniformly non-amenable. We study the basic properties of this invariant; for example, its behaviour when passing to subgroups and quotients of G. We prove that the following classes of groups are uniformly non-amenable: non-abelian free groups, non-elementary word-hyperbolic groups, large groups, free Burnside groups of large enough odd exponent, and groups acting acylindrically on a tree. Uniform non-amenability implies uniform exponential growth. We also exhibit a family of non-amenable groups (in particular including all non-solvable Baumslag–Solitar groups) which are not uniformly non-amenable, that is, they satisfy FølG=0. Finally, we derive a relation between our uniform Følner constant and the uniform Kazhdan constant with respect to the left regular representation of G.