The collapse conjecture for finite simple groups

Let $G$ be a finite group. Say that $G$ collapses if every finite-dimensional pointed Hopf algebra $H$ with group of grouplikes $G(H)\simeq G$ is isomorphic to $\Bbbk G$; equivalently, every nonzero Yetter–Drinfeld module $V\in {}^{\Bbbk G}_{\Bbbk G}\mathcal{YD}$ has infinite-dimensional Nichols algebra $\mathscr B(V)$. Collapse conjecture. If $G$ is a non-abelian finite simple group, then $G$ collapses. This conjecture would provide a guiding principle for the classification of finite-dimensional pointed Hopf algebras over non-abelian finite simple groups; the stated passage presents it as supported by evidence accumulated over the preceding years, without recording a resolution.