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Mathematics
Linear and Abstract Algebra
Cosets: Is [gH] a Subgroup of G?
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[QUOTE="Stephen Tashi, post: 5449128, member: 186655"] Always check the trivial cases. If you pick ##g_1## to be the identity element, the coset ##g_1H = H##, so it is possible for a coset to be a group. In fact, what happens when you pick ##g_1## to be any particular element of ##H## ? The interesting cases will be when ##g_1## is not an element of ##H##. If you try an example, you'll see that the coset ##g_1H## is not a subgroup of G because it does not contain the identity element of ##G##. Can you prove this defect always happens ? [/QUOTE]
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Forums
Mathematics
Linear and Abstract Algebra
Cosets: Is [gH] a Subgroup of G?
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