Hi I'd like to show that SU(n) is a normal subgroup of U(n). Here are my thoughts: 1)The kernel of of homomorphism is a normal subgroup. 2)So if we consider a mapping F: G-> G'=det(G) 3)Then all elements of G which are SU(n), map to the the identity of G', therefore SU(n) is a normal subgroup of GL(n,C). Firstly, is this correct? Also, a very stupid question, but can I ask whether my musings constitute a formal 'proof'? I mean, would I need to show prove statements (1) and (2) (ie. show it obeys the homom. property) or can I just say that I've assumed that they are for the purposes of the proof at hand? Thanks.