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arXiv · 2607.11775

A Torsion-free Supersoluble Group with Trivial Outer Automorphism Group

Mattia Brescia·Ernesto Ingrosso·Marco Trombetti
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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 $\Out(G)=1$.

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Mattia Brescia, Ernesto Ingrosso, Marco Trombetti. 2026-07-13. A Torsion-free Supersoluble Group with Trivial Outer Automorphism Group. https://arxiv.org/abs/2607.11775

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