1. The problem statement, all variables and given/known data Let G be a group. Show that G/Z(G) [itex]\cong[/itex] Inn(G) 3. The attempt at a solution G/Z(G) = g^{n}Z(G) for some g ε G and for any n ε N choose some g^{-1} such that g(g^{-1}h) = g(hg^{-1}) and the same can be done switching the g and g^{-1} This doesn't feel right at all...
I don't see what this has to do with the problem?? Can you find a surjective homomorphism [tex]f:G\rightarrow Inn(G)[/tex] and then apply the first isomorphism theorem?
No, not right. Given an element g of G can you name an inner automorphism of G corresponding to g? When do two different elements of G, g1 and g2 give define the same automorphism?