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?
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?
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.