Jump to ContentJump to Main Navigation
Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
Users without a subscription are not able to see the full content.

Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2017. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see http://www.universitypressscholarship.com/page/privacy-policy).date: 11 December 2017

Mil nor's problem on the growth of groups and its consequences

Mil nor's problem on the growth of groups and its consequences

Chapter:
(p.705) Mil nor's problem on the growth of groups and its consequences
Source:
Frontiers in Complex Dynamics
Author(s):

Rostislav Grigorchuk

, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159294.003.0025

This chapter presents a survey of results related to John Milnor's problem on group growth. The notion of group growth first appeared in 1955 in a paper of A. S. Schwarz, but it remained virtually unnoticed for over a decade. The situation changed after Milnor's papers from 1968, which sparked significant interest in this area. Particularly influential were two problems raised in these papers: the characterization of groups of polynomial growth and the question of the existence of groups of intermediate growth. The chapter discusses the cases of polynomial growth and exponential but not uniformly exponential growth; the main part of this chapter 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) are considered, and a number of open problems are suggested.

Keywords:   group growth, polynomial growth, intermediate growth, exponential growth, manifold growth, amenability, asymptotic behavior, random walks

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.