Affine Module Groups and Their Automorphisms

An affine module group is a semidirect extension of an additive module group by its automorphism group. Maximal Abelian normal subgroups of an affine group are described. It is proved that operator isomorphisms of affine groups are induced by module automorphisms. Automorphisms of an affine group which do not leave a module fixed are treated. And conditions are specified for a module to be non-characteristic in its affine group.