0
$\begingroup$

Possible Duplicate:
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian

If $G$ is a group such that $ (a \circ b)^i = a^i \circ b^i $ for three consecutive integers $i$, and $\space\forall a,b \in G$ , then show that $G$ is abelian. Then show this conclusion does not follow if "three" is replaced with "two".

  • 0
    Well what have you tried? Is this homework?2012-08-29
  • 0
    @OldJohn Indeed, and exact duplicate2012-08-29
  • 1
    @JohnMartin: It isn't exact - it doesn't take care of the finial sentence `Then show this conclusion does not follow if "three" is replaced with "two".'2012-08-29
  • 0
    @user1729: If $G$ has exponent 3, then $(ab)^3 = 1 = 1\cdot 1 = a^3 b^3$ and $(ab)^4 = ab = a^4 b^4$.2012-08-29
  • 0
    i have proved in similar way, as given in above link. But i want know different approach. But now it look like mine is approach is good and less confussing2012-08-29

0 Answers 0