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ON A NONABELIAN BALOG–SZEMERÉDI-TYPE LEMMA

Part of: Probabilistic methods in group theory Special aspects of infinite or finite groups Sequences and sets

Published online by Cambridge University Press:  08 June 2010

TOM SANDERS
TOM SANDERS*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK (email: t.sanders@dpmms.cam.ac.uk)
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Abstract

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We show that if G is a group and A⊂G is a finite set with ∣A2∣≤K∣A∣, then there is a symmetric neighbourhood of the identity S such that Sk⊂A2A−2 and ∣S∣≥exp (−KO(k))∣A∣.

Keywords

Balog–Szemerédi–Gowers lemmanonabelian groupsnoncommutative groupsapproximate groupKatz–Koester trickinduction on doublingFreĭman’s theorem

MSC classification

Secondary: 11B13: Additive bases, including sumsets 20F05: Generators, relations, and presentations 20F99: None of the above, but in this section 20P99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 1 , August 2010 , pp. 127 - 132
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

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