A Torsion-free Supersoluble Group with Trivial Outer Automorphism Group

Mattia Brescia; Ernesto Ingrosso; Marco Trombetti

A Torsion-free Supersoluble Group with Trivial Outer Automorphism Group

Group Theory 2026-07-13 v1

Authors: Mattia Brescia , Ernesto Ingrosso , Marco Trombetti

Abstract

We give a negative solution to Problem~13.23 of the Kourovka Notebook. We construct a torsion-free group $G$ of Hirsch length $14$ admitting a finite series $1=G_0\triangleleft G_1\triangleleft\cdots\triangleleft G_{14}=G$ in which every $G_i$ is normal in $G$ and every factor is infinite cyclic, but such that $\Out(G)=1$ .

Keywords

torsion-free group supersoluble group outer automorphism group Hirsch length Kourovka Notebook

Cite

@article{arxiv.2607.11775,
  title  = {A Torsion-free Supersoluble Group with Trivial Outer Automorphism Group},
  author = {Mattia Brescia and Ernesto Ingrosso and Marco Trombetti},
  journal= {arXiv preprint arXiv:2607.11775},
  year   = {2026}
}

Comments

15 pages