NORMAL AUTOMORPHISMS OF A FREE METABELIAN NILPOTENT GROUP

An automorphism phi of a group G is said to be normal if phi(H) = H for each normal subgroup H of G. These automorphisms form a group containing the group Of inner automorphisms. When G is a non-abelian free (or free Soluble) group, it is known that these groups of automorphisms coincide, but this is not always true when G is a free metabelian nilpotent group. The aim of this paper is to determine the group of normal automorphisms in this last case.