Polynomial Automorphisms of Soluble Groups

Abstract

A polynomial automorphism of a group G is an automorphism of the formWhen G is polycyclic, we prove that the set PAut G of all polynomial automorphisms forms a polycyclic subgroup of the automorphism group Aut G . When G is soluble, PAut G is not necessarily a subgroup, but we show that the subgroup generated by PAut G is soluble. We also give the general form of an element of PAut G when G is a torsion-free non-abelian metabelian nilpotent group.