Sieve methods in group theory I: Powers in linear groups

A general sieve method for groups is formulated. It enables one to ``measure'' subsets of a finitely generated group. As an application we show that if \Gamma is exponentially small. This is a far-reaching generalization of a result of Hrushovski, Kropholler, Lubotzky, and Shalev.

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Bibliographic Details
Published in:Journal of the American Mathematical Society 2012-10, Vol.25 (4), p.1119-1148
Main Authors: LUBOTZKY, ALEXANDER, MEIRI, CHEN
Format: Article
Language:English
Subjects:
Arithmetic progressions
Automorphisms
Eigenvalues
Group theory
Homomorphisms
Mathematical theorems
Prime numbers
Random walk
Vertices
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Summary:A general sieve method for groups is formulated. It enables one to ``measure'' subsets of a finitely generated group. As an application we show that if \Gamma is exponentially small. This is a far-reaching generalization of a result of Hrushovski, Kropholler, Lubotzky, and Shalev.
ISSN:0894-0347
1088-6834
DOI:10.1090/S0894-0347-2012-00736-X