What is the conjecture

https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.18

Suppose that $G$ is a finite group, and let $A \subset G \times G$ be a subset of density $\alpha$. Is it true that there are $≫_α |G|^3$ triples $x, y, g$ such that $(x, y), (gx, y), (x, gy)$ all lie in $A$?

AMS categories

• ams-05
• ams-11
• ams-20

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• I plan on adding this conjecture to the repository
• This issue is up for grabs: I would like to see this conjecture added by somebody else