# On cap sets and the group-theoretic approach to matrix multiplication

@article{Blasiak2016OnCS,
title={On cap sets and the group-theoretic approach to matrix multiplication},
author={Jonah Blasiak and Thomas Church and Henry Cohn and Joshua A. Grochow and Christopher Umans},
journal={ArXiv},
year={2016},
volume={abs/1605.06702}
}
• Published 21 May 2016
• Mathematics, Computer Science
• ArXiv
In 2003, Cohn and Umans described a framework for proving upper bounds on the exponent ω of matrix multiplication by reducing matrix multiplication to group algebra multiplication, and in 2005 Cohn, Kleinberg, Szegedy, and Umans proposed specific conjectures for how to obtain ω = 2. In this paper we rule out obtaining ω = 2 in this framework from abelian groups of bounded exponent. To do this we bound the size of tricolored sum-free sets in such groups, extending the breakthrough results of…
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