Triangles in Cartesian Squares of Quasirandom Groups. (25th August 2016)

• Record Type: Journal Article
• Authors: BERGELSON, V.; ROBERTSON, D.; ZORIN-KRANICH, P.
• Is Part Of: Combinatorics, probability and computing. Volume 26:Number 2(2017:Mar.)
• Page Start: 161
• Page End: 182
• Publication Date: 2016-08-25
• Subjects: Primary 05D10, -- Secondary 28D15; Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548316000250
• Languages: English
• ISSNs: 0963-5483

Abstract

Abstract : We prove that triangular configurations are plentiful in large subsets of Cartesian squares of finite quasirandom groups from classes having the quasirandom ultraproduct property, for example the class of finite simple groups. This is deduced from a strong double recurrence theorem for two commuting measure-preserving actions of a minimally almost periodic (not necessarily amenable or locally compact) group on a (not necessarily separable) probability space.