2 problems

Let $G$ be a group with norm $\|\cdot\|$, and let $F(G)$ denote the free group on the underlying set of $G$, with generators written $\overline g$. For $g_1,\dots,g_n\in G$, compar…

Let $G$ be a group equipped with the bi-invariant metric norm $\\|\cdot\\|$. For elements $g_1,\dots,g_n\in G$, consider the sequence of normalized norms of products of equal power…