On finite sets of small tripling or small alternation in arbitrary groups
On finite sets of small tripling or small alternation in arbitrary groups
Abstract We prove Bogolyubov–Ruzsa-type results for finite subsets of groups with small tripling, | A 3 | ≤ O (| A |), or small alternation, | AA −1 A | ≤ O (| A |). As applications, we obtain a qualitative analogue of Bogolyubov’s lemma for dense sets in arbitrary …