Thread: left and right cosets
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Old November 4th, 2009, 04:57 PM
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Originally Posted by jmoney90 View Post
No, the cosets are the easy part lol, I just wanted to make sure I was correct in my assumption that I only need to work out 2 cases (3 possible variations, and 1 of them is my subgroup H). I was just validating that I can be lazy rather than work out all 12 possible cosets
Haha, what is the point of theorems and corrolarys if you can't be a little lazy?

But think about it. We know that the relation which describes the concept of a coset (specifically a\sim b\Longleftrightarrow a^{-1}b\in H for left and a\sim b \Longleftrightarrow ab^{-1}\in H for right) is an equivalence relation. So it partitions G. So you'll know your done finding cosets when they've exhausted the elements of G
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