Giovanni Cutolo: papers

This couple of papers, once again written with my friends from South Wales, is on a classical question about the possible (abstract, algebraic) structure of automorphism groups of groups: trying to discriminate groups that are from groups that are not isomorphic to the full automorphism group of a group. Both papers stem from the guess that the dihedral group of order 8 is rather special in being of the former species, among the groups in the classes indicated by the titles. Indeed, for each of the two cases considered, it comes out that this is the only example if we restrict to the universe of finite groups; and even in the general case it has very few companions (only one for the case treated in [16]; of course the cyclic factors of the wreath products here are assumed nontrivial).