Amey Bhangale, Prahladh Harsha, Sourya Roy

In this note, we show the mixing of three-term progressions $(x, xg, xg^2)$ in every finite quasirandom group, fully answering a question of Gowers. More precisely, we show that for any $D$-quasirandom group $G$ and any three sets $A_1, A_2, A_3 \subset G$, we have

\[ \left|\Pr_{x,y\sim G}\left[ x \in ...
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