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Triangles in Cartesian Squares of Quasirandom Groups

Part of: Extremal combinatorics Measure-theoretic ergodic theory

Published online by Cambridge University Press:  25 August 2016

V. BERGELSON ,
D. ROBERTSON  and
P. ZORIN-KRANICH
V. BERGELSON
Affiliation:
Department of Mathematics, Ohio State University, 231 W. 18th Avenue, Columbus OH 43212, USA (e-mail: [email protected], [email protected])
D. ROBERTSON
Affiliation:
Department of Mathematics, Ohio State University, 231 W. 18th Avenue, Columbus OH 43212, USA (e-mail: [email protected], [email protected])
P. ZORIN-KRANICH
Affiliation:
Universität Bonn, Mathematisches Institut, Endenicher Allee 60, D-53115 Bonn, Germany (e-mail: [email protected])
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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.

MSC classification

Primary: 05D10: Ramsey theory
Secondary: 28D15: General groups of measure-preserving transformations
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 2 , March 2017 , pp. 161 - 182
Copyright
Copyright © Cambridge University Press 2016 

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