A finite divisible group is trivial
I am having trouble seeing why a finite divisible group is necessarily trivial. Why does this have to be the case?
Let $n=|G|$. If $g\in G$, then by divisibility there exists $h\in G$ with $h^n=g$. But $h^n=1$.
I am having trouble seeing why a finite divisible group is necessarily trivial. Why does this have to be the case?
Let $n=|G|$. If $g\in G$, then by divisibility there exists $h\in G$ with $h^n=g$. But $h^n=1$.