1. ## normal subgroup

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

2. Originally Posted by apple2009
If H is a subgroup of a finite group G of index [G: H] two, then H is normal in G.
Hint - What can you say about right and left cosets of H? And, hence about H.

3. Originally Posted by aman_cc
Hint - What can you say about right and left cosets of H? And, hence about H.
To prove for normal, I need to have the right cosets equal to right cosets, is the two left cosets are the cyclic and I?

4. what is the two left and right coset there?