Let $G$ be a finite abelian group of order $n$ with identity $e$. If for all $a\in G$, $a^3=e$, then by induction on $n$, show that $n=3^k$ for some non-negative integer $k$.
I am competely stuck on this. Please help anybody.
Let $G$ be a finite abelian group of order $n$ with identity $e$. If for all $a\in G$, $a^3=e$, then by induction on $n$, show that $n=3^k$ for some non-negative integer $k$.
I am competely stuck on this. Please help anybody.