Consider the cyclic group Cn = <g> of order n and let H=<gm> where m|n.
How many distinct H cosets are there? Describe these cosets explicitly.
Lagrange's Theorem: |G| = |H| x number of distinct H cosets
The Attempt at a Solution
|G| = n
I'm unsure if I have interpreted H correctly, I think it is the cyclic group generated by gm so contains gmk for integers k. I don't know how I can work out the order of H from this, or how to describe the cosets.