Index of subgroup H is 2 implies.... 1. The problem statement, all variables and given/known data Just had my abstract algebra test. This was the only question I did not answer. The rest I answered somewhat confidently. Prove that if H is a subgroup of G, [G : H] = 2, a,b are in G but not in H, then ab is in H. 2. Relevant equations 2 is the index of H, that is, the order of G equals 2 times the order of H. 3. The attempt at a solution I have no idea where to start with this. I can't even come up with a concrete example demonstrating this.