(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Lagrange's Theorem: |G| = |H| x number of distinct H cosets

3. 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.

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# Homework Help: Cosets and cyclic groups

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