Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Approximate multiplicative groups in nilpotent Lie groups


Authors: David Fisher, Nets Hawk Katz and Irine Peng
Journal: Proc. Amer. Math. Soc. 138 (2010), 1575-1580
MSC (2010): Primary 20-XX; Secondary 05-XX
DOI: https://doi.org/10.1090/S0002-9939-10-10078-1
Published electronically: January 19, 2010
MathSciNet review: 2587441
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We generalize a result of Tao which describes approximate multiplicative groups in the Heisenberg group. We extend it to simply connected nilpotent Lie groups of arbitrary step.


References [Enhancements On Off] (What's this?)

  • [1] A. I. Malcev, On a class of homogeneous spaces, Amer. Math. Soc. Translation 1951 (1951), no. 39, 33. MR 0039734
  • [2] M. S. Raghunathan, Discrete subgroups of Lie groups, Springer-Verlag, New York-Heidelberg, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68. MR 0507234
    M. Ragunatan, \cyr Diskretnye podgruppy grupp Li., Izdat. “Mir”, Moscow, 1977 (Russian). Translated from the English by O. V. Švarcman; Edited by È. B. Vinberg; With a supplement “Arithmeticity of irreducible lattices in semisimple groups of rank greater than 1” by G. A. Margulis. MR 0507236
  • [3] Terence Tao and Van Vu, Additive combinatorics, Cambridge Studies in Advanced Mathematics, vol. 105, Cambridge University Press, Cambridge, 2006. MR 2289012
  • [4] Terence Tao, Product set estimates for non-commutative groups, Combinatorica 28 (2008), no. 5, 547–594. MR 2501249, https://doi.org/10.1007/s00493-008-2271-7
  • [5] Terence Tao, Structure and randomness, American Mathematical Society, Providence, RI, 2008. Pages from year one of a mathematical blog. MR 2459552

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20-XX, 05-XX

Retrieve articles in all journals with MSC (2010): 20-XX, 05-XX


Additional Information

David Fisher
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: fisherdm@indiana.edu

Nets Hawk Katz
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: nhkatz@indiana.edu

Irine Peng
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: kanamejun@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-10-10078-1
Received by editor(s): January 29, 2009
Received by editor(s) in revised form: June 7, 2009
Published electronically: January 19, 2010
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.