Thread: Tell me how to do this proof.

It's hard...

Oh, you must know group theory and symmetry groups in order to attempt this.

Let sigma = (1 2 3 ... n) be in S_n (a cycle) with n>=1. Let k be a positive integer.

Show that if k is relatively prime to n, then sigma^k (with the operation being composition, obviously) is a cycle, that is, sigma applied k times can be written as one cycle of length greater than one composed with possibly a bunch of disjoint cycles of length 1.

Any ideas?

Um, could you put that into LaTeX and post an image of the equation? The wording is really confusing.

Originally Posted by ninja9578

Um, could you put that into LaTeX and post an image of the equation? The wording is really confusing.

There's no equation...words are just words.

The only thing even remotely resembling as equation is (1 2 ... n ) e S_n, where e is actually "is an element of". But the notation (1 2 ... n ) is cycle notation and is exactly how I wrote it.