2 problems

Let $G$ be a finite group, let $G^n$ denote its $n$-th direct power, and let $A$ be a generating set of minimum size for $G^n$. Write ${\mathrm{rank}}(G)$ for the minimum size of a…

Let $G$ be a finite group, let $G^n$ denote its $n$-th direct power, and let $D(G^n)$ denote the diameter with respect to a generating set, using words in that set. Write…