# Group theory, subgroup question

1. Jun 7, 2010

### rallycar18

Let A be a subgroup of G. If g $$\in$$ G, prove that the set {g$$^{-1}$$ ag ; a $$\in$$ A} is also a subgroup of G.

Thanks for any help.

Last edited: Jun 7, 2010
2. Jun 7, 2010

### Staff: Mentor

What's the definition of a subgroup?

3. Jun 7, 2010

### rallycar18

Thanks, mark- i left that out.

A subset A of a group (G,*) is called a subgroup if the elements of A form a group under *.

* is the binary operation of the two groups.

4. Jun 7, 2010

### Office_Shredder

Staff Emeritus
You have two choices:
1) Either prove that the set is a group by confirming that it satisfies all the group axioms (there are only four, so that's not too bad)

2) Use a theorem that allows you to confirm something is a subgroup in fewer steps (I don't know if you know any)

Just focusing on 1, can you for example prove that the identity is contained in that set?