群上的Bi-Lipschitz等价度量及加性数论中的一个问题
Bi-Lipschitz equivalent metrics on groups, and a problem in additive number theory
摘要：
有一个标准的“字长“度量规范地关联到组的任何生成器集合。具体地，对于大于1的任何整数a和b，整数的加法群具有分别与度量d_A和d_B相关联的生成集{a^i}_{i=0}^{\infty }和{b^j}_{j=0}^{ \infty }。证明了这些度量是双Lipschitz等价的当且仅当存在正整数m和n使得a^m = b^n.
英文摘要：
There is a standard "word length" metric canonically associated to any set of generators for a group. In particular, for any integers a and b greater than 1, the additive group of integers has generating sets {a^i}_{i=0}^{\infty} and {b^j}_{j=0}^{\infty} with associated metrics d_A and d_B, respectively. It is proved that these metrics are bi-Lipschitz equivalent if and only if there exist positive integers m and n such that a^m = b^n.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
