# On the polynomial automorphisms of a group

## TL;DR

This paper proves that for nilpotent or metabelian groups, the subgroup of automorphisms generated by polynomial automorphisms retains the same structural property, being nilpotent or metabelian.

## Contribution

It establishes that polynomial automorphisms generate a subgroup preserving the nilpotent or metabelian nature of the original group.

## Key findings

- Polynomial automorphisms form a subgroup that is nilpotent if the original group is nilpotent.
- Polynomial automorphisms form a subgroup that is metabelian if the original group is metabelian.
- The subgroup generated by polynomial automorphisms inherits key structural properties of the original group.

## Abstract

We prove that if a group is nilpotent (resp. metabelian), then so is the subgroup of its automorphism group generated by all polynomial automorphisms.