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## Homework Statement

Consider the cyclic group C

_{n}= <g> of order n and let H=<g

^{m}> where m|n.

How many distinct H cosets are there? Describe these cosets explicitly.

## Homework Equations

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 g

^{m}so contains g

^{mk}for integers k. I don't know how I can work out the order of H from this, or how to describe the cosets.