Let $G$ be a group such that for all $a$, $b$ $\in$ G, there exists $f$$\in$ Aut(G) satisfy $b$=$f(a)$.
i) Prove that if there is nontrivial élément in $G$ of finite order, then there exist prime number $p$ such that every nontrivial element in $G$ has order $p$
ii) Prove that if G is finite,then G is abelian p-group
I guess that we prove i) using cauchy theorem, but for ii) i have no idea how to prove it. I nead help to prove ii) in detail by giving some hints