- #1

- 768

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**Index of subgroup H is 2 implies....**

## Homework Statement

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.

## Homework Equations

2 is the index of H, that is, the order of G equals 2 times the order of H.

## 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.