Possible Duplicate:
Let$G$ is a group, $a$ and $b$ are non-unit elements of $G$, $ab=bba$. …
Let $G$ be a group and $a,b\in G$ such that $ |a|=3, ab=b^2a, b\neq e. $
What can I say about $|b|$?
What I get so far is something like $ ba^2=a^2b, ab^2=b^4a. $ I suspect that one can not determine $|b|$, but I'm not able to give a proof.