3 problems

Centralizer-count and derived-order conjecture. If

Centralizer–commutator conjecture. If

Let $G_{1}$ and $G_{2}$ be finite groups, and let $Pr^{2n}(G)$ denote the generalized commuting probability of $G$ at level $2n$. Write $Z(G)$ for the center of $G$. The conjecture…