Growth in groups: ideas and perspectives

Abstract

This is a survey of methods developed in the last few years to prove results on growth in non-commutative groups. These techniques have their roots in both additive combinatorics and group theory, as well as other fields. We discuss linear algebraic groups, with SL_2(Z/pZ) as the basic example, as well as permutation groups. The emphasis lies on the ideas behind the methods.

60 pages. This is the final version, incorporating corrections from the proofreaders. To appear in Bull. Am. Math. Soc

References in corpus (12)

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• Growth in finite simple groups of Lie type of bounded rank
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• On higher order Fourier analysis
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• Expansion in $S{L}_d(O_K/I)$, $I$ square-free
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• Generalization of Selberg's 3/16 Theorem and Affine Sieve
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• On growth in an abstract plane
• Freiman's theorem in an arbitrary nilpotent group