The Group Spencer conjecture for regular representations

Let $G$ be a finite group of size $n$, and let $A_1,\dots,A_n$ be the $n\times n$ matrices corresponding to the regular representation of $G$. Group Spencer conjecture. The Matrix Spencer conjecture holds for this particular choice of matrices. This is a group-theoretic special case motivated by the general Matrix Spencer conjecture. It is known for simple groups, while the general case remains open.