Abstract. Let ${\rm A}(G)$ denote the automorphism group of a group $G$. A polynomial automorphism of $G$ is an automorphism of the form $x\mapsto(v_{1}^{-1}x^{\epsilon_{1}}v_{1})\ldots(v_{m}^{-1}x^{\epsilon_{m}}v_{m})$. We prove that if $G$ is nilpotent (resp. metabelian), then so is the subgroup of ${\rm A}(G)$ generated by all polynomial automorphisms.

AMS Subject Classification (1991): 20F28, 20F16, 20F18

Keyword(s): polynomial automorphism, metabelian group, nilpotent group, IA-automorphism

Received February 14, 2006, and in revised form June 9, 2006. (Registered under 5954/2009.)