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arXiv · 2210.05488

A Note on Slice Rank and Matchings in Groups

Kevin Pratt
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Abstract

A multiplicative 3-matching in a group $G$ is a triple of sets $\{a_i\}, \{b_i\}, \{c_i\} \subset G$ such that $a_ib_jc_k = 1$ if and only if $i=j=k$. Here we record the fact that $\text{PSL}(2,p)$ has no multiplicative 3-matching of size greater than $O(p^{8/3})$, yet the slice rank of its group algebra's multiplication tensor is at least $Ω(p^3)$ over any field. This gives a negative answer to a conjecture of Petrov.

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Kevin Pratt. 2022-10-11. A Note on Slice Rank and Matchings in Groups. https://arxiv.org/abs/2210.05488

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