3
$\begingroup$

Define a permutation $\alpha\in S_n $ to be regular if either $\alpha$ has no fixed points and it is the product of disjoint cycles of the same length, or $\alpha=(1)$.

Prove that $\alpha$ is regular if and only if $\alpha$ is a power of an n-cycle.

It is a homework question in J.J.Rotman's book: A first course in abstract algebra with applications.

I have just begun reading the book, and I find this question confusing----I've tried using induction, but couldn't figure out a good way. I would really appreciate your help.

  • 0
    In the future it might be a good idea to try to say what about the question you found confusing.2012-07-15

1 Answers 1