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??
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 $\displaystyle e \neq a \in G$ and apply the induction hypothesis to the quotient group $\displaystyle \frac{G}{<a>}.$
Last edited by NonCommAlg; Apr 22nd 2009 at 12:04 AM.