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~小弟我所學有限~~希望能幫上你的忙
Let H be a subgroup of a finite group G.
Now we define an equivalence relation a~b if and only if ab^(-1) is in H.
So we can make the partition of G with this equivalence relation.
For each partition is a right coset of H, Ha = {ha : h in H}
Check:
For any h1a,h2a in Ha,h1a(h2a)^(-1)=h1aa^(-1)h2^(-1)= h1h2^(-1) is in H, so h1a and h2a are equivalence. So for each right coset is a equivalence class. ... |
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