On the cardinality of sumsets in torsion-free groups

Details On the cardinality of sumsets in torsion-free groups On the cardinality of sumsets in torsion-free groups

2010-09-30

arxiv.org/abs/1009.6140v1

Mathematics

Group Theory

Scientific paper

Let $A, B$ be finite subsets of a torsion-free group $G$. We prove that for every positive integer $k$ there is a $c(k)$ such that if $|B|\ge c(k)$ then the inequality $|AB|\ge |A|+|B|+k$ holds unless a left translate of $A$ is contained in a cyclic subgroup. We obtain $c(k)

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