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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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A new proof of Gromov’s theorem on groups of polynomial growth
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by Bruce Kleiner PDF
J. Amer. Math. Soc. 23 (2010), 815-829 Request permission

Abstract:

We give a new proof of Gromov’s theorem that any finitely generated group of polynomial growth has a finite index nilpotent subgroup. The proof does not rely on the Montgomery-Zippin-Yamabe structure theory of locally compact groups.
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Additional Information
  • Bruce Kleiner
  • Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012-1185
  • Email: bkleiner@cims.nyu.edu
  • Received by editor(s): May 29, 2009
  • Published electronically: December 28, 2009
  • Additional Notes: The author was supported by NSF Grant DMS 0701515.
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 23 (2010), 815-829
  • MSC (2010): Primary 20F65, 20F69, 20F67, 20F18
  • DOI: https://doi.org/10.1090/S0894-0347-09-00658-4
  • MathSciNet review: 2629989