Possible Duplicate:
Problem from Armstrong's book, “Groups and Symmetry”
If $a$, $b$ are members of the permutation group $S_n$, and $ab=ba$. Show that $b$ must be a power of $a$ when $a$ is an $n$-cycle.
Possible Duplicate:
Problem from Armstrong's book, “Groups and Symmetry”
If $a$, $b$ are members of the permutation group $S_n$, and $ab=ba$. Show that $b$ must be a power of $a$ when $a$ is an $n$-cycle.