In Lagrange's Theorem, it states that the order of G is the number of cosets of H in G multiplied by the order of H.(adsbygoogle = window.adsbygoogle || []).push({});

What I don't understand is what if H is just a subgroup among other elements in G? Let's say there is some k in G then kH consists of all the left cosets of H. But there is also m in G that do not go into any cosets. Then how can the order of G only include the left cosets?

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# Homework Help: Lagrange's Theorem

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