Gromov's theorem on groups of polynomial growth and elementary logic
Gromov's theorem on groups of polynomial growth and elementary logic
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关于多项式增长群和初等逻辑的格罗莫夫定理
DOI：
10.1016/0021-8693(84)90223-0
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发表时间：
1984
影响因子：
0.9
通讯作者：
A. Wilkie
中科院分区：
文献类型：
--
作者：
L. Dries;A. Wilkie
在1980年秋天的作者参加了教授山雀'当然在耶鲁大学，他给了一个帐户格罗莫夫的美丽的证明，每一个非线性生成组的多项式增长有一个幂零子群的有限指数。一个重要部分格罗莫夫的论点包括建设每个小组的多项式增长的一个局部紧度量空间和行动的一个子群的有限指数的空间。这种构造背后的直观动机是相当清楚的，但它需要一个精心设计的度量空间“极限”理论来实现。
In the fall of 1980 the authors attended Professor Tits’ course at Yale University in which he gave an account of Gromov’s beautiful proof that every finitely generated group of polynomial growth has a nilpotent subgroup of finite index.An essential part of Gromov’s argument consists of constructing for each group of polynomial growth a locally compact metric space and an action of a subgroup of finite index on that space. The intuitive motivation underlying this construction is fairly clear but it required an elaborate theory of “limits” of metric spaces to be carried out.