Complete outer automorphism groups of free nilpotent groups

TL;DR

This paper proves that the outer automorphism group of an infinitely generated free nilpotent group of class two is a complete group, meaning it has trivial center and every automorphism is inner.

Contribution

It establishes the completeness of the outer automorphism group for a broad class of infinitely generated free nilpotent groups of class two.

Findings

Outer automorphism group is complete for infinitely generated free nilpotent groups of class two.

The group has trivial center and all automorphisms are inner.

The result extends understanding of automorphism groups in nilpotent group theory.

Abstract

We prove that the outer automorphism group $\mathrm{Out}(N)$ of an infinitely generated free nilpotent group $N$ of class two is complete.