My Question Reads:
Let G be a group and let AutG be the set of all automorphisms of G. Also, let InnG be the set of all inner automorphisms of G. Prove that InnG is a subgroup of AutG.
My thoughts:
I believe I would need to first state the definitions of an automorphism which is a function from a group to itself and an inner automorphism is where again a function from G to itself occurs but where f(a)=c^-1*a*c.
From here I am not too sure if I need to then prove closure and inverse to confirm subgroup but I am confused how to do this considering these are the type of functions I am dealing with.
For closure, would I need to pick two inner automorphisms or am I still picking two values of G?