Product set phenomena for countable groups

2013/09/17 by Björklund, MIchael, Fish, Alexander · 1 citation
#05C81 #11B13 #11K70 #37B05 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1309.4262

Abstract

We develop in this paper general techniques to analyze local combinatorial structures in product sets of two subsets of a countable group which are "large" with respect to certain classes of (not necessarily invariant) means on the group. As applications of our methods, we extend and quantify a series of recent results by Jin, Bergelson-Furstenberg-Weiss, Beiglböck-Bergelson-Fish, Griesmer and DiNasso-Lupini to general countable groups.

Cited by

• Discrete sumsets with one large summand

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