Talk:Complete group

If someone has time, both Rotman and Robinson group theory texts have a nice little discussion of complete groups and the automorphism tower problem. It would be good to mention the tower problem and add an explicit reference or two. JackSchmidt 01:43, 30 August 2007 (UTC)

Injective and surjective
Do there exist groups G that are isomorphic to their own automorphism groups but such that the canonical homomorphism from G to Aut(G) is injective but not surjective, or surjective but not injective? GeoffreyT2000 (talk) 23:24, 8 May 2015 (UTC)