Abstract Algebra - Subgroups of index 2 in R*

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Homework Statement

I am having trouble understanding how I would go about finding all subgroups of index 2 in R*, the multiplicative group of nonzero real numbers. Any hints will be greatly appreciated.

Homework Equations

The Attempt at a Solution

 

[Hurkyl]

If you don't know what you need to do, then look for something you can do.

For example, you spent a lot of time dealing with structure theorems for Abelian groups -- so one of the most natural things to do when studying an Abelian group is to see if you can analyze its structure...