Milnor's Problem on the Growth of Groups and its Consequences

Details Milnor's Problem on the Growth of Groups and its Consequences Milnor's Problem on the Growth of Groups and its Consequences

2011-11-02

arxiv.org/abs/1111.0512v2

Mathematics

Group Theory

version 2 extends previous

Scientific paper

We present a survey of results related to the Milnor's problem on group growth. We discuss the cases of polynomial growth, exponential but not uniformly exponential growth, but the main part of the article is devoted to the intermediate (between polynomial and exponential) growth case. A number of related topics (growth of manifolds, amenability, asymptotic behavior of random walks) is considered, and a number of open problems is suggested.

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