Bounds for Matchings in Nonabelian Groups

  • Will Sawin
Keywords: Finite groups, Sum-free sets, Slice rank


We give upper bounds for triples of subsets of a finite group such that the triples of elements that multiply to $1$ form a perfect matching. Our bounds are the first to give exponential savings in powers of an arbitrary finite group. Previously, Blasiak, Church, Cohn, Grochow, Naslund, Sawin, and Umans (2017) gave similar bounds in abelian groups of bounded exponent, and Petrov (2016) gave exponential bounds in certain $p$-groups. 

Author Biography

Will Sawin, Columbia University / Clay Foundation
Department of Mathematics, Assistant Professor and Clay Research Fellow
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