Kneser's Theorem in σ-finite Abelian groups

2019/11/18 by Bienvenu, Pierre-Yves, Hennecart, François
#11P70 (primary) 11B05 #20K99 (secondary) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1911.07745

Abstract

Let G be a σ-finite abelian group, i.e. G=\bigcup_{n≥ 1} G_n where (G_n)_{n≥ 1} is a non decreasing sequence of finite subgroups. For any A⊂ G, let \underlined(A):=\liminf_n→∞(|A∩ G_n|)/(|G_n|) be its lower asymptotic density. We show that for any subsets A and B of G, whenever \underlined(A+B)

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