1. The problem statement, all variables and given/known data If G is a group and aϵG, then the inner automorphism θa: G --> G is defined by θa(g) = aga-1. Let Inn(G) = group of inner automorphisms and Z(G) = the centre of G. Use the Isomorphism theorem to show G/Z(G)≅Inn(G). 2. Relevant equations 3. The attempt at a solution Firstly, the inner automorphism θa: G --> G defined by θa(g) = aga-1 is a group homomorphism, with its kernel being the centre of G, denoted Z(G). And its image = Inn(G). So since the theorem says Im(θ) ≅ G/ker(θ), then G/Z(G)≅Inn(G). Would I have to somehow prove that Z(G) = ker(θ)? I don't really know where to begin. Likewise with Im(θ) = Inn(G). Please let me know if this attempt is sort of close to the actual solution. Thankss!!!