论文标题
切片排名和小组匹配的注释
A Note on Slice Rank and Matchings in Groups
论文作者
论文摘要
组$ g $中的乘法3匹配是$ \ {a_i \}，\ {b_i \}，\ {c_i \} \ subset g $的三倍，使得$ a_ib_jc_k = 1 $，仅如果$ a_ib_jc_k = 1 $，则仅如果$ i = i = j = j = k $。在这里，我们记录了一个事实，即$ \ text {psl}（2，p）$没有大于$ o（p^{8/3}）$的乘法3匹配，但其组的乘法张量至少为$ω（p^3）$。这给了彼得罗夫的猜想带来负面答案。
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.
