2 problems

Let $G$ be a non-abelian finite simple group, and let $S_1,\dots,S_k$ be normal subsets of $G$. Normal product decomposition conjecture. There exists $c$ such that, whenever … one…

Let $G$ be a non-abelian finite simple group, and let $S_1,\dots,S_k$ be subsets of $G$. Ideal product decomposition conjecture. There exists $c$ such that, whenever … there exist…