# Math Help - group order problem...

1. ## group order problem...

Q:Let G be a finite abelian group of order n with identity e,If for all a belongs to G,a^3=e then by induction on n show that n=3^k for some non negative integer k??

2. Originally Posted by Mathventure

Q:Let G be a finite abelian group of order n with identity e,If for all a belongs to G,a^3=e then by induction on n show that n=3^k for some non negative integer k??
Hint: to complete the induction choose any $e \neq a \in G$ and apply the induction hypothesis to the quotient group $\frac{G}{}.$