If H is a subgroup of a finite group G of index [G: H] two, then H is normal in G.

I need to show that the left cosets equals to the right cosets, but what are the cosets here?

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- Nov 8th 2009, 06:11 PMapple2009normal subgroup and cosets
If H is a subgroup of a finite group G of index [G: H] two, then H is normal in G.

I need to show that the left cosets equals to the right cosets, but what are the cosets here? - Nov 9th 2009, 12:10 AMNonCommAlg
there are more than one way to prove this. one way is to write where let if then clearly so we may assume that for some

then now if for some then which is a false result. so and we're done.

by the way, i just realized that you've already posted this question in here. next time don't post your question twice.