Thread: isomorphic

how do i prove that if the centre of a group G is trivial then inn G is isomorphic to G.

can i say that if the centre of the group G is trival, then the quotient is G itself.
using the fact G/ centre is iso to InnG, we conclude that G is iso to inn G

Yes, that's right. Show that there's a homomorphism from G onto Inn(G) (given by conjugation), then that the kernel of this map is the center of G. Then use first isomorphism.