2 problems

For every finite simple nonabelian group $G$, there exists a conjugacy class $C$ of $G$ such that $C^{2}=\{xy:x,y\in C\}=G$.

Godara and Sarkar conjectured that, for every odd prime $p$, if $H_{p^3}=\operatorname{UT}_3(\mathbb{F}_p)$ is the Heisenberg group of order $p^3$, then $\mathsf{d}(H_{p^3})=3p-3$,…