Small doublings in abelian groups of prime power torsion

2019/01/17 by Yifan Jing, Jing, Yifan, Souktik Roy +1
Engineering · Mathematics · #05D05 #11P70 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1901.05606

openalex publication_date 2019/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a subset of G, where G is a finite abelian group of torsion r. It was conjectured by Ruzsa that if |A+A|≤ K|A|, then A is contained in a coset of G of size at most r^CK|A| for some constant C. The case r=2 received considerable attention in a sequence of papers, and was resolved by Green and Tao. Recently, Even-Zohar and Lovett settled the case when r is a prime. In this paper, we confirm the conjecture when r is a power of prime. In particular, the bound we obtain is tight.

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