期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2021
卷号：21
语种：English
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：In this note, we show the mixing of three-term progressions (xxgxg2) 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 A1A2A3G , we have PrxyGxA1xyA2xy2A3−3i=1PrxGxAi 2D41 Prior to this, Tao answered this question when the underlying quasirandom group is SLd(Fq). Subsequently, Peluse extended the result to all nonabelian finite simple groups. In this work, we show that a slight modification of Peluse's argument is sufficient to fully resolve Gower's quasirandom conjecture for 3-term progressions. Surprisingly, unlike the proofs of Tao and Peluse, our proof is elementary and only uses basic facts from nonabelian Fourier analysis.
