Group theory, subgroup question

[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.

 

[Mark44]

What's the definition of a subgroup?

 

[rallycar18]

What's the definition of a subgroup?

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.

 

[Office_Shredder]

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?