Triangles in cartesian squares of quasirandom groups

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.

16 pages

References in corpus (8)

• Further applications of the Container Method
• Lower bound in the Roth theorem for amenable groups
• Quantitative equidistribution for certain quadruples in quasi-random groups
• Finite Products Sets and Minimally Almost Periodic Groups
• Idempotent ultrafilters and polynomial recurrence
• Mixing and double recurrence in probability groups
• Ajtai-Szemerédi Theorems over quasirandom groups
• The Ultraproducts of Quasirandom Groups

Cited by in corpus (3)

• Uniform syndeticity in multiple recurrence
• The Ultraproducts of Quasirandom Groups
• Corners over quasirandom groups