@article{b53fd45ff13f4327a902010d17d8f4fc,

title = "A Finitary Version of Gromov's Polynomial Growth Theorem",

abstract = "We show that for some absolute (explicit) constant C, the following holds for every finitely generated group G, and all d > 0: If there is someR0 > exp(exp(CdC)) for which the number of elements in a ball of radius R0 in a Cayley graph of G is bounded by R d0then G has a finite-index subgroup which is nilpotent (of step < Cd). An effective bound on the finite index is provided if {"}nilpotent{"} is replaced by {"}polycyclic{"}, thus yielding a non-trivial result for finite groups as well.",

keywords = "Polynomial growth, harmonic functions, nilpotent groups",

author = "Yehuda Shalom and Terence Tao",

note = "Funding Information: 1.15 Acknowledgments. The authors thank Emmanuel Breuillard for valuable discussions, and the anonymous referee for corrections. The first author was supported by ISF and NSF grants number 500/05 and DMS-0701639 resp. The second author is supported by a grant from the MacArthur Foundation, by NSF grant DMS-0649473, and by the NSF Waterman award.",

year = "2010",

month = dec,

doi = "10.1007/s00039-010-0096-1",

language = "אנגלית",

volume = "20",

pages = "1502--1547",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "6",

}