Question

abstract algebra

Abstract algebra: Let T be an m-cycle ( 1 2 3 ... m ) , show that T^i is an m-cycle if m,i are
relativity prime

Answer 1

hmn. So, T^i is the permutation that maps the kth element of the set to the k+ith element of the set (modulo the number of elements) ?

Answer 2

i suppose so

Answer 3

I'm not sure actually. I haven't done this in a while. According to my book, an m-cycle is a permutation (bijective map) of elements a1, a2,..., ak, such that a1 maps to a2, a2 maps to a3, etc...

Answer 4

But I think I've got something wrong. Maybe with T^i. Since I can come up with some counter-examples... Sorry.

Answer 5

I recommend going through your notes and making absolutely certain you understand how these things are defined. In algebra, I find that makes up a major part of proving something. If you still can't see it from that, then I recommend posting on here what the exact definitions are for these things, that your teacher gave you, and then maybe someone can help.

Answer 6

okay, thanks