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Approximate multiplicative groups in nilpotent Lie groups
Author(s):
David
Fisher;
Nets
Hawk
Katz;
Irine
Peng
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1575-1580.
MSC (2010):
Primary 20-XX;
Secondary 05-XX
Posted:
January 19, 2010
MathSciNet review:
2587441
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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:
-
- [1]
- Malcev, A. I., On a class of homogeneous spaces. Amer. Math. Soc. Translation 1951 (1951). no. 39, 33 pp. MR 0039734 (12:589e)
- [2]
- Raghunathan, M. S., Discrete Subgroups of Lie Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68. Springer-Verlag, New York-Heidelberg, 1972. MR 0507234 (58:22394a)
- [3]
- Tao, Terence; Vu, Van, Additive Combinatorics. Cambridge Studies in Advanced Mathematics, 105. Cambridge University Press, Cambridge, 2006. MR 2289012 (2008a:11002)
- [4]
- Tao, Terence, Product set estimates for non-commutative groups, Combinatorica 28 (2008), no. 5, 547-594. MR 2501249
- [5]
- Tao, Terence, Structure and Randomness: Pages from Year One of a Mathematical Blog, American Mathematical Society, 2008. MR 2459552
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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:
10.1090/S0002-9939-10-10078-1
PII:
S 0002-9939(10)10078-1
Received by editor(s):
January 29, 2009,
Received by editor(s) in revised form:
June 7, 2009
Posted:
January 19, 2010
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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